Welcome to the forums!
I have replied to your other post on the Lovebird Lovers section.
I'm glad you managed to rescue the lovebird. From your description on the interactions between the lovebird and your budgie, it's highly likely the lovebird had close contact with other species of pet birds on its previous home.
Despite the fact the lovebird is friendly to your budgie, it's still best to house him on a separate cage. This is done for your budgie's safety as well as your rescued lovebird. If the budgie is pecking, the lovebird may get tired of it and peck back and do harm to the budgie due to its much bigger and powerful beak.
Have you tried to find this lovebird's owner? You can place fliers on your neighbourhood, and nearby pet stores/vets stating you have found a lovebird.
For now you should get a cage for the lovebird and quarantine him for at least 1 month in order to prevent any possible illness to be spread to your budgie.
If you can't locate the owner and will keep the lovebird, then after quarantine time is over and depending on your lovebird and budgie's behaviour, you can let them have closely supervised out of cage time together. Even if they get along well, it's always best to house them in separate cages. The cages can be close by so they can see and communicate with each other.