lmer analysis of identical twins data

We have PFAS measured pollution dataset constructed of ~50 (n=100) monozygotic (identical) twins. 
The goal is to detect the significantly differential PFAS pollutants between the leaner individuals (L) and 
those individuals with obesity (F):

 'pfasLogStandardized ~  LF + sex + youngOrOld + yearClass +  (1 | familyID)'.

This is the correct approach, given this is a cotwin-control design. You might first check the magnitude of the twin intraclass correlation, but I think it very unlikely that you can ignore genetics and shared environment. How has zygosity been diagnosed? The model can be extended if you have dizygotic twins present as well.

Cheers, David Duffy.