It is not easy for birds of two other types to mate but it could happen when they are caged and are kept as a couple. Even if they mate with each other, it is not necessary that the female would lay fertile eggs. The best part is that both are friends so there is no life threat involved in putting both in same cage. You can try and see what happens.

They are usually in different cages next to each other. When the lovebird is released during the day, the female budgie keeps calling him. He feeds her mouth to mouth from outside her cage.

Sometimes I try to put them together. I see the lovebird is afraid to approach the budgie who does not like to be approached. She pecks him, but he never bites her.