Could a man be a lesbian?

In this question, MissAnthrope comments:

I’ll be honest, having a penis and getting to play with it would be a main highlight [of having your gender changed]. I think everyone has their own perspective and, being a lesbian and getting intimate with women, obviously there are some limitations (easy and enjoyable to work around, but limitations nonetheless). One ex of mine, she and I had the most mind-blowing sexual connection and we talked a fair amount about kind of wishing we had a penis sometimes. I don’t know how to describe it, but I was so into her, so in love.. giving her pleasure was over-the-moon awesome, yet I wanted so badly to know what it would be like to really feel her. With all my feelings for her, I could only imagine it being supremely amazing.

I replied: ”Now the idea that a lesbian might want a penis to help pleasure her lover and herself is quite fascinating. It kind of raises the issue of what it means to be a lesbian; in specific: would it be possible for a man to be a lesbian?”

There are “women in men’s bodies.” Men, who truly believe they are or should have been women. Often they are gay, but what if they were interested in both women and being a woman?

And there’s the trip the other way around. A lesbian might want to be a man so she could pleasure her partner more mindblowingly. If she became a man, would she still be a lesbian?

Underlying this is the whole notion of gender. Is it more related to your mind, or to the configuration of your body? In either case, how do they interact in your case, in terms of your gender identity?