It’s a common misconception that a pet bird needs another bird for a “friend”. Lovebirds are of course a species of parrot, and adult parrots do not have friends. Once they are mature enough, they have a mate. Before that, they interact some with flock members, but that stops once they have a mate. Even when you have same sex birds together in captivity, they will eventually form a close bond and lose interest in human interaction. If you get another lovebird, you are getting it for a future mate for Luna, or for a companion for yourself.
Luna needs to be kept away from a baby lovebird – she is likely to kill it. Lovebirds are somewhat misnamed. Even the pairs bicker a lot. But a lovebird will kill another one in a minute if they don’t like it. Luna has no use for a baby lovebird in her territory. Luna is the typical territorial female lovebird. Most likely when she flies to the budgie cage, she is much more interested in fighting with them than interacting. As far as she is concerned, they are in her territory, and rivals that do not go away are killed. Definitely never let her near those budgies if they are out of the cage. For that matter, female budgies can be just as aggressive. The female from your bonded pair will be a danger to a baby lovebird. While an adult lovebird is going to win in a fight with a budgie, an adult female budgie is likely to overpower a baby lovebird because the baby will be scared.
Getting a new lovebird will also make Luna’s biting worse. First because she is jealous to have this baby in her territory. Later if the new bird is a female, Luna probably won’t like that. If it’s a male, she may or may not bond with it once it is mature at around 1-2 years old. If you want this new lovebird to remain tame, then you can never cage it with Luna. If they bond, you will never be able to handle either of them again. I know it’s a lot to think about & I’m not saying that you shouldn’t get another bird, but understand it is more for you than for Luna.
Thank you for asking Lafeber,