Does an abbreviation which is written in lowercase have to be capitalised after a period? [duplicate]

Whenever you encounter a situation where a "rule" (such as begin a sentence with an upper case letter) will reduce the readability of your test (Is MESC the same as mESC?) then rewrite. Do not try to find a loophole or a special rule that will need to be explained or justified. The meaning of your text is paramount.

There is a reason why chemistry texts do not begin a sentence about acids and bases with pH.

According to Scientific Style and Format: The CBE Manual for Authors, Editors, and Publishers (C B E Style Manual),

Even if the editor chooses a style that calls for initial capitalization of every term, some terms should retain an initial lowercase letter. [...] 3 A standard symbol or abbreviation that begins with a lowercase letter (pH, pK', mRNA).

Also, according to apsstylemanual.org,

An abbreviation that begins with a lowercase letter, or a term that must remain lowercase should not be changed to all caps when it begins a sentence; it should not be expanded. The word following should be is lowercase unless it is a proper noun or another acronym. If possible, reword the sentence so that it does not begin with the lowercase term

I don't see anything (other than the one regarding brand names) in the Chicago Manual of Style.