The lizard is not an alligator lizard. It is a female blue belly also known as northern fence lizard.
The incident with the alligator lizard-- including the method of extraction-- is based on an actual incident that occurred to science fiction/fantasy writer Seanan Mcguire while she was a reptile rescue volunteer.
Jim Parrack (Judd Ryder) and Dominic Burgess (Dave Sheffield) both guest starred on Supernatural (2005-2020), Jim as a monster (Episode 4.04) and Dominic as a human villain (Episode 13.15).