Here’s my new post on Anole Annals, with video of an unusual interaction between a fan-throated lizard and an Indian robin. The Indian robin chases after the lizard, as though attempting to peck at the lizard’s tail. Most interactions between fan-throated lizards and robins do not proceed like this–at most, the lizards display at passing robins, and robins, in turn, usually ignore the lizards.
But my colleague Sreekar Rachakonda. has published this note on Oriental Magpie-Robins–he has observed magpie robins eating house geckos! Indian robins are a bit smaller than magpie robins, but perhaps they still attempt to feed on lizards? Judging by the usual interactions between fan-throated lizards and Indian robins, however, these birds likely don’t prey on lizards too often.
Ambika Kamath 
I live in New Mexico, and in the Jemez mountains I’ve observed American Robins eat lizards.