Hi Ege, that's kind of you to look after your relative's lovebird.
Think about what you can do differently so that the bird doesn't feel the need to bite you. He should give plenty of body language to warn you he is not happy with what you are doing before he bites. It is up to you to read and heed it. It sounds like you are going too fast too soon. Watch his body language... does it remain relaxed when you approach him? If not, rethink your approach. You may have to approach slower or lower.
What does he go for in the food bowl first? These will be his favourite foods. If he likes apple, try wedging a whole slice through the cage bars. When he's ok with eating that, make the slice smaller and smaller so that eventually he is taking just a small piece from your fingers. Always start with a big treat so that he doesn't have to get too close to your fingers and then break it down smaller when he's taking the treat nicely from you. Feeding through the cage bars will offer you both protection. Once he is taking the treat, you can start training anything you want. Targeting is a good one to start with.
As Brian pointed out, lots of birds don't like hands inside their cages - it is their territory.