From what has been said even if it isn't suspicious, what she is asking is illogical. If her identity is male then they cant say they are a lesbian. And without getting into detail if you identify as male, and have undergone surgery then no actual lesbian is going to accept you. Being lesbian is about being same sex attracted, ie to the female body. Not sure how much intimate detail the group goes into, and maybe some dont think that!
Nor can they use a lesbian support group to try and make friends. That derails the group and again asks women to give up their right to have support to become someone else's support.
I appreciate that she may be in need of support, but isn't there not a trans group in the area she could join.
It maybe that she is regretting transitioning, but again to support her in that changes the purpose of the group.
And if it is because she is having difficulty to find women to get involved with, then that is something she going to have to work through. That some heterosexual women will not want to be in a relationship with her, and neither will some lesbians.
I echo the suggestions up thread about some of the members of your group taking time to meet her and talk with her, and to ask her quite genuinely why is she says she identifies as male she can say she is a lesbian. And can she understand how confused you all are about how she can ask this.
(And of course, where and how she found out about the group.)
This does make me wonder whether there are any trans men support groups. So much noise and demands are about trans women not trans men.
This also brings up some sad memories of a women's group I was part of that came about for a particular project, and it just happened that everyone was lesbian. It was fairly thankless and time consuming work. And then just towards the end one of the women suddently announced they were about to transition, and said she realised she could not longer be part of the group and we were unlikely to see her again. We were all stunned, as had not had any notion that this was something she was considering, and probably didn't respond well. And we all just sort of stood there saying, how said it was that this was goodbye. This was 25/30 years ago.