What is an animal that is cold blooded and is a vertebrate?

Coldblooded vertebrates include the fish, the amphibians and the reptiles.

There are a actually fish with lungs, lungfish. Some species of lungfish have more or less working gills, but most species need to breath using their lung(s) even when in the water.

Amphibians all have a juvenile water-breathing form, no exceptions to my knowledge. Their adult form has lungs.

Reptiles (crocodiles, snakes, lizards, turtles) are the group you are probably looking for. These breath using their lungs.