The Big Lizard disaster is unlocked by burning 100 tons of garbage at an incinerator. This is from the IGN guide on achievements:
What's Cookin'? - Burn 100 tons of garbage in an Incinerator at the
Garbage Dump to gain access to the Big Lizard disaster
In my personal experience so far, he has done the same thing to my city. He made a beeline for the garbage dump, causing death, fire, and destruction all along the way. After he ate a bunch of garbage, he burrowed into the ground and left. Him eating garbage actually DOES decrease the amount of tons of garbage you have stored in your dump.
It would seem that his appearance might become more likely with the more garbage you keep piled up, however, earlier tonight he appeared without a garbage dump at all. His appearance was brief, he burrowed into the ground in a residential area, and was done. He sure is an interesting creature.