I had a similar problem with my U2 Echo. He would get very possessive over objects. And become very aggressive with them and me. I made up a little game of give and take with him, where I would reward him when he gave me things. I have no idea if that would work with a lovebird though.
If You wanna try it you begin with a low value object, something they have some interest in but not overly possessive about. Then slowly work you're way up to more interesting things. It's a game we still play and there are some high value objects that he won't give up on but I'm able to take them away from without the fear of being bitten. Which for me is the whole point of the game. So as long as he show no signs of aggression he gets praised.
Echo's come along way, he use to try and bite my face when I took something away from him. Now he enjoys giving me stuff usually of low value stuff. But he never trys to bite me when I take away more highly valued stuff.
I m still working desensitizing certain objects with him. And I'm learning new stuff about him and what makes him tick. But I'm very happy with how well our relationship is going