I honestly cannot understand why someone would still consider herself a lesbian even when dating men. That makes her bi. If she can't admit that she has an interest in both men and women and is therefore bi (or pansexual, or queer, or primarily gay, or questioning, or bi-curious or homosexual but heteroromantic, whatever) - there's some issue going on, and that alone would make me wary.
Anyway, no, I would not date a lesbian. She would want a woman, I'm not a woman, and if she thinks I'm close enough I don't want to be in a relationship with her.