Ivan, here are my thoughts in response to your questions.
Because lice are super-small bugs, a lice-comb needs to have VERY-FINE teeth to be effective at combing the lice out of human hair. (See the photo below.) Without seeing photos of the two metal combs you found, showing the size of the teeth on them, I can't say whether they are a lice-comb or a hot-comb.
Your theory that perhaps a hot-comb would be used to remove lice from hair is a reasonable-sounding one... but I think that if the metal comb was hot enough to sizzle the lice, it would also sizzle the hair.
I agree that it's "curious" that one of your metal combs is marked "Marine Medicine Co." I did a websearch for that name, to see if I could find info on that company's products, and its time-period... but I got no web results at all. Perhaps somebody else here will be able to find some historical information about that company.
As the Wikipedia article indicates, a hot-comb's purpose was to straighten kinky (or very-curly) hair. For anybody who doesn't already know... in the latter-1800s through early-1900s, hot-combs were popular with African-Americans who wanted to make their (naturally kinky) hair resemble the long smooth "flowing" hair of Caucasians ("White folks).
The photo below shows a lice-comb, made of "hard rubber," which was listed as being from the civil war era. However, I should mention (for anybody here who doesn't already know) that a patent-date on a relic only tells us the EARLIEST date that the relic was manufactured. The comb in the photo was made by the IR (India-Rubber) Comb Company... which was in business from 1852 to 1898. So, although the patent-date on that lice-comb is 1851, it could have been manufactured by the IR Comb Co. several years after the civil war ended (1865).