I've had my lovebird (peachfaced) for 5 years.
No DNA test but I am positive it is a male, as he has never exhibited the nest building behaviors of stuffing things in his feathers, even when his hormonal behaviors were so constant it was problematic!
My lovebird, while independent, is also very tame and enjoys being a part of our every day life. However, if we are outside the cage and he is in, he will run over and run his beak up and down the bars, acting like he wants to nip. And he will give you a nip if he gets a hold of you in this situation, but he has never, not a day in his life, given me a nip so hard as to draw blood. And I can recall only a few times he gave me one that actually hurt.
I do believe this 'cage aggression' behavior is normal (especially for a lovebird) and not entirely avoidable. As long as they behave themselves when I open the door, I am happy. And he does. I taught him to 'come here' and step up on my finger on his own without any prodding from me in about twenty minutes (smart little birds!).
I don't believe it is possible to keep a tame lovebird if you have it living together with other birds. They tend to bond very strongly, and of course stronger to their bird friends. I have yet to see or hear of a truly tame lovebird pair. I have seen that other members have multiple lovebirds, but I do not know if they are all tame, and if they are kept together.
My favorite trick is to bring a chair and sit next to the cage. Then I put my hand in the cage with their favorite treat on it and just sit and wait. I don't move, don't stare constantly at the birds, and rarely talk. This is how I began taming several completely wild budgerigars. It does work with the little birds.
Just knowing lovebirds in general, and being that the shop I used to frequent had many but none were tame (she loved my little guy because she said he is the first lovebird she has met that never bites), I have my doubts that any lovebird not handled from a very young age will ever be a pet quality bird.