Have you ever seen a full size adult American Alligator? They are not small animals. They are also not exactly known to be friendly care free animals. Can you imagine having to get it looked at by a vet? I bet that would cost more than a Blue Eye Lucy itself.

If you are going to do it do it right and just get you a Saltwater Croc.

BTW, just because something is legal does not mean that there are not permits and permissions needed to do it. With that Im not saying it is or isn't legal for you to own one. I don't support the idea enough to google it for you.