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In Ancestry.com's England & Wales, Non-Conformist and Non-Parochial Registers, 1567-1970 there is an image from Piece 4330: Chelsea Hospital (Church of England non-parochial), 1691-1765 which records the death of a Jeremiah Smith who was buried on 31 Dec 1747 at Chelsea Hospital, London, England.
After his name are the letters "L.H.M.".
On one other name on the same page are the letters and abbreviation "L.H.Man".
What might these mean?
I believe L. H. M. stood for Light Horse Man. This was a rank of light-armed soldier.
There are numerous references to this rank in Chelsea Hospital and its Traditions (1838).
Just for your interest – a light horseman of that era would have looked something like this 1791 sketch (source British Museum):
I would encourage you to browse through other pages in the register to get an idea of what other types of ranks were listed (I would do it myself but unfortunately don't have access to Ancestry currently). This could help determine whether this is likely correct or not.
On the advice of @HarryVervet I browsed more pages through until 1750 and found many instances of "L.H.Man" but no other "L.H.M.".
A few pages before Jeremiah Smith's entry I found one for an "L.H. Mans Boy" and then on 7 May 1747 a "Light Horse Man":
