It seems that there are some types of Dragon Lairs (at least 2, maybe a third one). Each type provides a different kind of dragon, once you buid a camp (or "monument") in there.
Dont get confused with the so-called "monument" buildings: One is built inside of the city, to expand ZoC, and the other is built in the "Prestigious Location" to provide influence. They both have no relation with dragons. It is just a semantic issue.
We have asked many times the name of at least one of the buildings to be changed, but devs seems to prefer people get confused and post again and again about it.