If you do not mind the mess, give your lovebird a piece of raw broccoli every day. My parakeets (budgies) love to chew on broccoli. It is a good toy as well as very nutritious for them with loads of vitamins and minerals.
Other useful toys you can get a piece of cuttle bone. These parakeets need their beaks trimmed constantly since it's growing nonstop. They like to chew on stuff to achieve this goal. Cuttle bone can work as a trimmer as well as the much needed calcium supplement for these pet birds. You can get cuttlebone from cuttlefish lol, or just buy it from a pet store either locally or from online sources.
You can also get some tree branches. Just make sure the particular tree species is not toxic or had been sprayed with pesticide.
