I think my friend has gone a little crazy..

I would simply sit her down and ask her why she suddenly wants to ask her with you ?
Tell her you thought she identified as a lesbian so why this sudden change of heart ?

It's possible she's been hurt by her ex girlfriends and now wants to give up on girls altogether (not that it's realistic if she is,indeed, a lesbian but could be what she is tryig to do right now)

Just have a chat with her and see what she says.

 

I agree, you just have to find a chance to properly talk to her about it. Telling her that you are not her boyfriend doesn't make anything better. How does she regard her sexuality, and how does she feel about you as a person/sexual partner/romantic partner?

In the meanwhile, you could tell us more about what you know so that maybe we can help you better. Just because she broke up with two women in the past 3 months doesn't necessarily mean she's in an unstable point in her life. It could've just been a casual thing that she broke off? We don't know your age but maybe she is just experimenting, which is perfectly healthy. Has she told you that she's depressed?

 

I can see the point that she might just be experimenting, but I have a bit of a different take on the situation. Regardless of whether she's experimenting with you or not, the amount of pressure she's putting on you to put out seems unhealthy, and that concerns me. You should to talk to any friends you have in common or her friends, to see if she's been acting differently around them as well. Is she acting normally aside from being really sexual with you? After reading this, I'm worried about your friend, too.

I've never been in your position before, but I can identify with your friend, we might have had a similar experience. I went through a really hard time a few years ago, in which I fell in love with my straight best friend. Our friendship was unhealthy, we were obsessed with each other, but she would always flirt with me "as a joke" and often crossed a line in doing so. That really fucked with my head, and things went downhill from there, eventually she forced it out of me. Every time I tried fixing things, they got worse. The months that followed were some of the darkest in my life. The parallel I see between me and your friend's story is that while I was depressed, I was really, really interested in my three good, female friends at the time. (Not all at once, but I went back and forth between them.) I think the attraction(s) arose because I had this huge void in my life, and I was desperate for distraction. I was never able to act on any of the attractions in the way that your friend did because two were actually straight. I did however get really touchy with them, especially with my bi friend, V, and looking back I feel really bad about it, because I must have made her really uncomfortable. I think if I had been more in a position to act on what I was feeling at the time, I might have used sex as a distraction, which is what I think your friend is doing. But, if her experience is anything like mine, she might regret this change in relationship with you when her rough patch has run in its course.

Hopefully my story helped you get some perspective about where she might be coming from! I realize my post was pretty long, so I'll boil my position down to one point: If you have moral objections to sleeping with her because of her mental state, it might be best to wait until you know more about what's going on in her head.