Either you two come clean and come out, making your relationship obvious to all and sundry, even family. And then this guy will probably back off.
Or you don't, and he won't.
I take it that just telling him and asking him to keep quiet is not on the table. So, you're left with the two scenarios above ^.
Are you in a society where being lesbians is not just frowned upon but downright dangerous? Then you either accept it will end some time, or you both leave the area.
If you don't live in such a society, and it's just family disapproval you're trying to avoid, you need to get over that. Your family/families may be more accepting than you think. And if they aren't, then you'll know something about the family, yes?
Let me add one more thing.
Regardless of what you want to do regarding your family and your relationship, if she's not interested in this guy, then she's got to make that clear, sooner rather than later. It's the only fair thing to do for him. At this point in time, this is at least a clear path to take. She needs to do a kindness for this guy and then the two of you have some decisions to make.