I used to live in Florida and it would get really damp and cold outside and cockroaches would begin appearing in my house every few days. Most of them were those huge flying palmetto bugs (which I don't think any type of lizard can choke down), but there were some small roaches too. We had always had a little ffamily of geckos that lived outside our house usually hanging around the porch light, sometimes even coming inside. They do eat insects, though I'm not too sure that they would get of an infestation. For the occasional bug seen in your house, the lizards probably get their fair share of meals out of them, but if the roaches are an everyday problem, you may need to call pest control!
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