Hmm...that's a tough one. I'm really a snake person, but I'll try to help you out. One option is to search Google with keywords like "lizard care sheet vegetable" and see what you come up with. I'm no expert, but I believe most lizards eat crickets or some other invert at some point in their lifespan. Iguanas are an exception to that, but they *do not* make good pets for most people, and especially not as a first lizard.
Personally, I wouls say either an Anole or a Bearded Dragon would be good lizards to start with. I'm not sure about the Anole, but Beardeds definitely do eat crickets. Maybe the best thing would be to talk to your mom about her aversion to inverts. I have a Monitor lizard who eats crickets and an occasional wax worm, but I don't keep them in the house. My local pet store gut loads their feeders, so I just buy them a few at a time when I need them. I have a bag of ten crickets on a shelf at home right now...but that's about as many as I ever have at a time. If you have a garage or shed you could keep them there. Crickets don't really chirp much, eiher, so they're not as noisy to keep as you'd expect.
Well, try that Google search, and also ask this question in one of the lizard forums. Good luck, and keep us posted!
0.2 Ball Pythons (Idunna & Freja), 1.2 Corn Snakes(Arden/Vanora & Liath), 1.0 Columbian Boa(Ruadh), 0.1 Rough Green Snake(Caoilin), 0.1 Trans-Pecos Rat Snake, 1.0 Western Hognose Snake(Perth), 0.1 Northern Blue-Tongued Skink