Possessive nouns that end in s can be difficult to navigate, even for those skilled in grammar. The difference between the three choices you listed lie in the punctuation of the word lover. We are choosing whether the correct punctuation for this word (in this context) should be lovers', lovers, or lover's. The correct placement (or lack of) the apostrophe makes up the difference between the choices.
Were we to choose lover's, that would indicate just one person. Since we know that there are two people in this phrase, that is not the correct answer. Lovers is also incorrect because it does not denote possession.
The correct answer in this case is "soul meets soul on lovers' lips." This placement of the apostrophe indicates that both lovers possess their own set of lips. Because lovers is a plural noun, we add an apostrophe but not an additional s.