Even while she is in the cage you could begin with target training to get her to follow you around the cage. This would also help with the relationship and trust between you two. You could even begin with a special treat whenever you approach the cage, so she begins to associate your presence with, well, presents

. Once she realizes that spending time with you is a good thing, she will begin to want to do it more, and you can progress to getting her to come to your hand and finger.
I would not change things in the cage for a while, to allow her to become comfortable in her new home.
And as Richard has advised, read any of the taming and training posts that look important to you and your bird, even if they are about other parrots. Patience and perseverence are the keys here. Keep at it and it will happen when your Lovebird is ready. Good luck, keep us posted on your progress!