As soon as she becomes dissatisfied, she will turn face and educate the OP about just how wrong it would be for her to stay with him. Sadly, the general consensus of "convert or nope out" sounds like what will end up happening.
I feel you on the loneliness.
Make sure she is Even after that, the Church discourages them from entering serious relationships before they are considering marriage. And no I would not pressure them to convert but as a Latter-day Saint I would pray for them to convert as I do for many people I know and love.