I was under the impression it was still a lizard.
Yes, just as you are still a vertebrate. Because that is the name given to the sort of worm-like guy that was the only vertebrate around once upon a time. The rules for naming clades (as I understand them) mean that you have to be one and stay one.
Likewise you are also a primate.
I’m not clear why you aren’t also a fish; perhaps there is a cladist who can explain that.