Firstly, a lesbian and a female-to-male transsexual are two vastly different things. A lesbian is a woman sexually/romantically interested in other women only. A female-to-male transsexual is a person who was assigned female at birth but identifies as a male and wishes to or has undergone medical/social transition to live as a man.
A transsexual man is a man, and can be of any sexual orientation (gay as in interested in other men only, bisexual, heterosexual as in interested in women only, etc.). Pre-transition, his appearance will probably be masculine in style, and some lucky dudes even pass as men before hormonal treatments, but that's not a given, and many pre-everything transsexuals choose to remain closeted in public and may only wish to be recognised as their target sex in smaller circles, such as amongst friends and family.
Your scenario seems to concern a pre-transition transman living in the male gender role publicly, as in, he has not undergone hormonal treatment or surgery of any kind to alter his physical sex, but prefers male pronouns and recognition as a man in social situations.
Dating him is dating a man. Due to his still explicitly feminine biology, a lesbian may find herself attracted to him and some transmen do date lesbians pre-transition. (Some transmen actually go through a phase where they identify as lesbians, because transsexuality is rare and homosexuality may seem like the more likely option - or the only one you know of.)
A lesbian, however, is unlikely to recognise him as a man and still stay attracted to him, because he is not a woman. Most often relationships like this fall apart.
I can give you a personal example: pre-transition and during the questioning phase, I dated a lesbian woman. When I figured out my identity and we discussed it, she tried to stay, but eventually found herself unattracted to me due to the very fact that in her mind, I had become a man, and she simply isn't into men. We broke up during my social transition, the phase where I started living in the masculine gender role.
Some heterosexual women find themselves attracted to pre-everything transmen. To them, the biological sex of their partner is less relevant than the gender identity and presentation. I know a few heterosexual women in relationship with transsexual men, from whom the most started dating before or during the man's transition from female to male.
Now, after hormonal treatments, an FtM will
appear a dude,
sound like a dude and
grow hair like a dude. Now no lesbian will find herself attracted to the guy, because they simply aren't women nor female. The transsexual man will likely not be seeking out any lesbians at this stage either, because that just seems like a wasted effort. Why the hell would he?
Whether or not the transsexual guy will go under the knife is irrelevant to this, but for the sake of it, let's entertain the thought of a transman who is on hormones and hasn't gone through bottom surgery. I'll start by saying that a large portion of transsexual men do not have surgery on their genitalia, because the surgery results aren't necessarily satisfying, and the risks in a surgery of this scale are big and it is a damn painful procedure with a very long recovery time. Most guys do get top surgery, as in the chest reconstruction/masculinization to remove breast tissue and get a proper male chest.
So our guy is very average and gets his chest done, but not his junk. Is the heterosexual-identifying woman dating him a lesbian for being into his junk?
Firstly, testosterone does things to a p***y. It naturally enlarges the clitoris and turns its appearance more p***s-y, in most cases enough to heavily differ from any natural female clitoris, and in some big enough to pass for a micropenis - some FtMs are able to penetrate with this. So, it's not exactly the female thing anymore, it's something in between there.
Secondly, when a p***y is attached to a person who in every other aspect appears male, its association with femalaness and, more, womanhood drops. It is entirely up to the woman's preferences. For some women, it is explicitly important that her partner, the man, has a biologically male body. They are not attracted to a person whose junk appears female. That is okay.
Then there are equally heterosexual women whose preferences aren't so much in the genitalia as they are in the overall appearance and presentation of the man they are attracted to. This is also okay, and does not change their sexual orientation even in the case they are attracted to a man who was born biologically female and retains his v****a.
Hopefully this lengthy response was of any use, either to OP or someone else.
