Please dont get a cat (or any other pet) unless you really LIKE them. Doing otherwise is cruel. Yes, most cats would kill lizards, but NOT ALL WILL DO THIS.
I live in Florida and we have tons of those lizards. I dont care for them myself and dont want them inside. IF I did, I would check out those lizard traps, because I DO have a cat that I love very much. Using flypaper or sticky sheets could end up hurting my cat. I used them on my patio for ants and lizards and ended up killing a little bird. I felt awful about that.
I think it is ridiculous to call in an "expert" for this problem. Dont even bother, because most pest control people dont even deal with lizards. I know this because I asked exterminators when I interviewed them for an ant problem.
I dont know if this would work for lizards but ants and other insects are killed using diatomaceous earth (food grade only!) It is totally safe for you, your children and any pets you have. Some people even eat this stuff (although I dont know why!) I have bought it on Ebay and it was quite cheap. Just make sure it is food grade because the DE made for swimming pools is toxic. You could Google this to find out if it works on lizards.