The first thing worth pointing out is that the mutant you saw in X3: The Last Stand and the Dr. Curt Connors from the original Spider-Man trilogy and the The Amazing Spider-Man films are not part of the same universe, thanks to the various rights issues between Sony Pictures (who own the live action rights to Spiderman and all related properties) and 20th Century Fox (who own the live action rights to X-Men and the Fantastic Four and all related properties (with some complex caveats)).
However, in the main Marvel Comics continuity and the Ultimate Universe, Spider-Man and the X-Men do indeed share the same world. As far as I am aware, a mutant with the specific power to quickly regrow limbs (such as the one see in X3: The Last Stand) has never been shown in the comics, but Wolverine himself has a healing factor that includes the ability to regrow limbs.
The problem here is that after his initial transformation into The Lizard, Dr. Curt Connors would re-transform into his bestial alter-ego frequently, with one trigger being stress or chemical reactions. Between his frequent retransformations into The Lizard, the ethical issues involved with experimentation on humans (and mutants), and the fact he has mainly only appeared in Spider-Man related comics, to the best of my knowledge, Dr. Curt Connors has never experimented on mutants.