My Flying Lizard is a pterodactyl-like memento that can be found in Silent Hill: Shattered Memories with "Lost World Terry" written on its tag. Harry Mason finds it inside the safe in the Fun & Games Toy Store in Toluca Mall.
There are other extinct animals in the game, like the Xerces Blue butterfly in the "Pinned Beauty" memento, or the bug trapped in amber in the "Suffocated Forever" memento. Sir Arthur Conan Doyle wrote a book called The Lost World about a part of the Amazon where dinosaurs and other extinct creatures still live. This could refer to Harry living on in Cheryl's mind. It is also a likely nod to the Air Screamer.
It could also be a reference to Michael Crichton, since there is a Crichton Street in Silent Hill. Crichton's book The Lost World, a sequel to Jurassic Park, is about scientists genetically engineering dinosaurs on a remote island.