From The Ethics of Diet by Howard Williams, 1883:

One of the most distinguished of the hygeistic and scientific promoters of the reformed regimen, Dr. Lambe, occupies an eminent position in the medical literature of vegetarianism, and he divides with his predecessor, Dr. Cheyne, the honour of being the founder of scientific dietetics in this country.

His family had been settled some two hundred years in the county of Hereford, in which they possessed an estate that descended to Dr. William Lambe, and is now [1883] held by his grandson. He early gave promise of his future mental eminence. Head boy of Hereford Grammar School, he proceeded, in due course, to St. John's College, Cambridge. In 1786, being then in the twenty-first year of his age, he graduated as fourth wrangler of his year. As a matter of course he was elected a Fellow of his college, where he continued to reside until his marriage in 1794. During this period of learned leisure he devoted his time to the study of medicine, and the MS. notes in the possession of his biographer, Mr. Hare, "prove the diligence with which he studied his profession, and there we see the origin of his enlarged views of the causes of disease, so much insisted on by these fathers of medicine, and so much neglected by modern physicians in their search for chemical remedies." After his marriage he went to reside and practice in Warwick, where he was the intimate friend of Parr, the well-known Greek critic, and of Walter Savage Landor, who writes of him as "very communicative and good humoured. I had enough talk with Lambe to assure myself that he is no ordinary man." It was to the discoveries of Dr. Lambe, and his publications reporting the curative value of its mineral waters, that Leamington owed its fame and popularity. . .

Like many other members from orthodox dietetics both before and after him, Dr. Lambe found himself impelled to experiment in the non-flesh diet by ill-health. His bodily disorders, indeed, were so complicated and of such a nature, as to excite astonishment that not only he greatly mitigated their violence, but that he also survived to an advanced age. . . his Additional Reports (writing in the third person), he informs us: "He resolved, therefore to finally execute what he had been contemplating for some time - to abandon animal food altogether, and everything analogous to it, and to confine himself wholly to vegetable food. This determination he put into execution the second week of February, 1806, and he has adhered to it with perfect regularity to the present time [written 1814].

In 1805, at the age of forty, we find him established in practice in London. Five years later he was physician to the General Dispensary, Aldersgate Street. He was also elected Fellow and Censor of the College of Physicians, whose meetings he regularly attended. His peculiar opinions did not tend to secure popularity for him, . . .

Not the least interesting fact in his life is his share in the conversion of Shelley, and his friendship with J. F. Newton and his interesting family, at whose house these earlier pioneers of the New Reformation were accustomed to meet, and celebrate their charming réunions with vegetarian feasts.

Amongst the most interesting correspondence of his later years is his interchange of ideas with Sylvester Graham - the first of the American prophets of the reformed regimen. The letter to the celebrated American vegetarian is, as Dr. Lambe's latest biographer justly observes, " a most valuable relic, because it continues the result of Dr. Lambe's diet up to September 1837. . .

For the connections between Lambe, Shelley J.F.Newton etc see Family Tree

From The Vegetable Passion, by Janet Barkas, 1975:

In 1809. . . the publication of Dr. William Lambe's report on the Effects of a Peculiar Regimen in Scirrhous Tumours and Cancerous Ulcers. His "peculiar regimen" consisted of a meatless diet, with a liberal use of distilled water. "We may conclude," Lambe wrote in his influential paper, "that it is the prosperity of this regimen, and in particular, of the vegetable diet, to transfer diseased action from the viscera to the exterior parts of the body - from the central parts of the system to the periphery. . . " Lambe listed the various ailments that may be eliminated by adopting a vegetarian diet - brain disease was just one of them.

From 'Vegetarian America - a history' by Karen and Michael Iacobbo, 2004:

Shelley [Percy Byshhe 1792-1822] . . . was influenced . . . by a friend, Dr. William Lambe, author of The Doctor's Moral Inquiries on the Situation of Man and Brutes. On the Crime of Committing Cruelty on Brutes, and of Sacrificing Them to the Purposes of Man, etc.

[re: William Andrus Alcott (1798-1859) author of The Vegetable Diet As Sanctioned by Medical Men and By Experience in All Ages.] - Alcott presented . . . evidence of the benefits of the diet from renowned physicians and scientists of his time and of the past, such as George Cheyne, William Lambe, Professor Lawrence, and Baron Cuvier.

While at Alcott House [1842]. . . With William Lambe, M.D., and surgeon J. N. Sherman, [A. Bronson] Alcott formed a vegetarian society named the Physiological and Health Association [presumably short lived as we have no other record of this]. . .

Lambe was a renowned physician in the UK and across the Atlantic in America. A letter he wrote in defense of vegetarianism, published in The Lancet, was also published in The Bulletin of Medical Science, a Philadelphia based periodical edited by John Bell, M.D.

The doctor wrote: "I apprehend it to be impossible for you not to know that the experience of all ages has proved that a healthy man can be perfectly nourished without using a particle of animal food. I will fearlessly assert, from long experience, that vegetable food is much more salubrious than mixed diet in common use, in which, however, animal matter commonly enters in the smallest proportion. Numerous instances may be cited of persons who have lived for years in very good health without animal food ..." - William Lambe, "On the Possibility of Supporting Life on a Vegetable Diet," The Bulletin of Medical Science 11 (October 1844): 339.

Englishman Lambe explained that since 1804 (sic) he had been a vegetarian - "induced to this by severe bodily suffering." Lambe, who was in his late 80s (sic) when he wrote to The Lancet, stated that he had been healthy the past 38 years due to his vegetable diet.

• LAMBE, 1765-1847 - from The Ethics of Diet by Howard Williams M.A.
• Water and Vegetable Diet in Consumption, Scrofula, Cancer, Asthma, and Other Chronic Diseases (1815) by Dr. William Lambe, First Pub. London 1815 as 'Additional reports on the effects of a peculiar regimen in the cases of cancer, scrofula, consumption, asthma and other chronic diseases.' This edition 1850 New York with intro by Joel Shew M.D.p.90/91: "My reason for objecting to every species of matter to be used as food, except the direct produce of the earth, is founded as may be seen in my last publication on the broad ground that no other matter is suited to the organs of man, as indicated by his structure. This applies then with the same force to eggs, milk, cheese, and fish, as to flesh meat."
• The Life of William Lambe M.D. (PDF 500k) - by E. Hare, 1873, complete text of the 1897 reprint.
  
  
• The Medico-chirurgical review, Volume 13, 1828 Edited by James Johnson
  Commentary on "An Investigation of the Properties of Thames Water". By William Lambe, M. D. 8vo. sewed, p. 66. 2s. 6d. 1828.
  [an extraordinary view of the spread of disease, 40 years before John Snow's first pamphlet on Thames water being the source of cholera. Snow had also been following Lambe's 'Water and Vegetable Diet' from 1830 when he was 17]
  
  99. Dr. Lambe On Thames And River Water.
  
  There being now but one opinion as to the impurity and insalubrity of the water with which a considerable portion of the metropolis is supplied, the minds of men are naturally led to inquire into the remedy. Dr. Lambe, who has long turned his attention to the properties of water and its extraneous admixtures, now presents us with a pamphlet, in which he has taken great pains to examine the water of the Thames, not only about London, but higher up, and beyond the reach of the tide—consequently where the Thames is in the same condition as other rivers. The inquiry is therefore interesting, as affecting not merely the water of the Thames, but of the New River, and, indeed of every river. The following "GENERAL CONCLUSION" we shall extract.
  
  "The result of the examination of the Thames water at London, has proved that every product of it which can be obtained and exhibited in a distinct form, is tainted, or to speak more truly, is wholly composed of the exuvua of animal and vegetable matter. We have extracted bodies which can be traced to no other origin out of the soluble saline matter; out of the insoluble residuum; out of the hardly soluble sulphate of lime; finally, out of that insoluble matter separated by simple boiling, and improperly called carbonate of lime. We have shown that the insoluble residuum itself is partly at least, if not totally, volatile at the low degree of heat of boiling water, a property which distinguishes it completely from all common earthy matter, and entitles it to be ranked among organic bodies. We have extracted from it oily substances, which can be traced to no other source than to the accumulation of organic remains. Finally, we have extracted abundantly the constant residuum of organic bodies, a charcoally matter, by the simple process of solution in acid (under peculiar circumstances) which I conceive could never happen but with a water deeply and incurably tainted with heterogeneous substances, deposited from the filth with which it is incessantly mingled. No man, therefore, I should think, who calls himself a chemist, or who aspires to the more exalted title of a philosopher, can have the hardihood to deny that this water is loaded with animal and vegetable putridity, in as high a degree as it is possible, in any which the human organs can sustain. And all those who, thinking with me, consider such matters to be deleterious and destructive of animal life, must join in condemning it as unfit to be applied to any dietetic purpose whatever.
  
  "If we trace the river higher up to the point where the tide nearly ceases to be observed, strong presumption has been afforded that the same mischief predominates, but in a somewhat mitigated form. Circumstances which have been already detailed have prevented my acquiring the evidence on this point which it was intended and desired. But I entertain no doubt that it will be established, that the pollutions of the river received at the metropolis are carried upwards as far as the influence of the tide extends."
  The water of the Thames at Windsor, does not appear to have been so minutely examined as the London water; but our author seems to conclude that both it and all other rivers "must become loaded with whatever soluble matter an abundant putrefaction can supply, wherever the said river or rivers run through a rich and fertile country with a dense population." While we cannot deny that a certain proportion of foreign and corrupt matters must necessarily exist in all streams that run through fertile soils, and near the habitations of men and animals, yet we apprehend that we can only balance between the greater and the lesser evil— and that we must and ought to be contented, if we can procure our general supply of water from such a running stream as does not pass through any large town. Dr. Lambe observes that there are only four modes of purifying foul water - chemical agents - boiling - filtration - distillation. The two first are out of the question; but, "filtration through charcoal frees water from putrid and perhaps from putrescent vapour, and so far must be preferable to every other mode of filtration."
  
  But Distillation is considered by Dr. Lambe as the only process which can render water perfectly pure and perfectly wholesome. Dr. L. has brought forward a considerable number of cases illustrating the beneficial effects of distilled water on cancer and other local affections; and the Doctor pretty openly accuses Mr. Abernetby of stealing from him the facts and information, " which have formed the ground-work of his present opinions." Dr. L. does not propose any scheme by which distilled water might be afforded, on a large scale, to the metropolis; the process, therefore, of distillation can only apply to that portion of water which is drunk by each individual, and this must be purchased. The present price of distilled water is 4d. per gallon; but Dr. L. thinks it might be procured at one fourth of that sum. The conclusion to which most men, we think, will come, is, that water should be supplied from a running stream, as the New River is now supplied; and that we must put up with such impurities as the filter cannot remove from it. We shall never cease, however, to hold up our hands against the Thames water taken up nearer than Windsor.