If I understand it well, you’re in love with someone who’s already engaged and you don’t know if and how to let her know of your feelings.
It is a really delicate situation, you should carefully consider the consequences. You say that she’s been a lesbian for only 3 years. Let’s get rid of the lesbian tag and say that she’s been in love for 3 years. From how you describe it, their relationship seems solid, although she seems not to be perfectly happy with it all the time. It’s normal in any relationships to sometimes have doubts and insecurities. You should feel honored that she shares it with you, but it’s what friends do.
She seems to like to spend time with you, maybe especially when she’s in a relationship crisis and get touchy-feely with you, but it doesn’t mean she’s in love. Maybe she lusts for you, but as long as she decides to stay in a relationship, maybe it would be wiser to respect it. As long as someone is in love with another, to meddle between them may cause a lot of trouble, maybe you would lose your friend over it. There’s a lot at stake. If she decides one day to break up with her girlfriend, then would be a better timing I think.
In any case, I wouldn’t hold my breath, you are still available to meet other girls, to have fun with them. If it’s meant to be, it will happen. Maybe now is not the time yet.
That’s my careful advice. Let’s see the bold side.
If you decide to tell her, she might either share your feelings or not.
If she feels the same about you, she might break up and go out with you. Because you feel that she’s your perfect match doesn’t mean it is, but it might be worth a shot, you might have a good relationship that might last, or not. But once you go past the friendship level, if love doesn’t work, it might never go back to friendship.
Now, if she doesn’t share your feelings, she might just tell you that she’s in a relationship, she’s not interested and/or that she sees you only as a friend. Which is not too bad IF it doesn’t change her attitude towards you. Because she might not be as comfortable around you anymore.
It’s all about what you’re willing to risk. If you risk nothing, you gain nothing but you keep what you have. Maybe it could pay off on the long run. If you risk everything, you might win, get even or lose. You’re the only one who can take this decision. I hope this will help your reflexion, feel free to write again!