I’ve seen this happen with lovebirds and other species. Even with a breeding pair, lovebirds tend to have a love/hate relationship. They squabble a lot. When caging more than one bird together, I always recommend having as many food and water dishes as birds, plus one extra food. So for your birds, I would have 3 food cups in different parts of the cage and two water cups. This keeps one bird from keeping the other away from food. At first, he might try to claim all 3 cups, but this turns into a lot of work and he will likely give up soon.
Since you think the one being picked on is older, this is possibly the cause. In a wild flock, a sick or weak flock member will be avoided and often driven away, because this is a weakness and could attract a predator. So your younger bird may just be following instinct to push away the older, less healthy bird. If the bullying becomes relentless, then you will need to separate them, but the cages can remain side by side. Watch for passive bullying – where the one bird moves next to the older bird until it moves away. Sometimes the bully will continue to follow the other bird around the cage, making the other bird very tired. You won’t notice this passive aggression unless you are watching for it. If both birds can fly, you can consider having the wings trimmed on the younger bird to slow it down – it is hard to say how much that would help since lovebirds can jump pretty far.
Thank you for asking Lafeber,