Son nom lui venait de sa peau diaphane que complimentaient

Son nom lui venait de sa peau diaphane que complimentaient des lèvres rouges. -- Her name came from her diaphanous skin that red lips complimented. / ...complimented by red lips.

There is an inversion in the relative clause, which means that subject and object change places. The subject is des lèvres rouges, in plural, which is why the verb is also 3rd person plural. The lips are doing something -- namely complimenting -- to her skin (that's what the relative pronoun que refers to).