In my case, I have seen a huge house lizard eating a live cockroach which was equally huge(presumably the American variety). The whole body was eaten except the wings! So, it's true, lizards do really get rid of cockroaches!! And it's also equally true, they leave big blobs of droppings everywhere!!! I have often stepped on the droppings even!!! And having lizards dropping on my feet when I watch TV is a common practice. In addition, they like to chase each other all over the walls in my house!!!!! And created a raucous racket! So, finally, I got so fed-up of them that I bought some lizard glue and placed them where they like to roam. It was successful and I have sometimes caught four lizards over a few days, both big and small. After the lizards were gone, the cockroaches came back! Then, I bought some cockroach bait and placed them where they like to frolic. Eventually, their numbers were down.