A quick, easy way to decide whether there was a chemical change
is to look and see whether there are NEW substances after the
event, that weren't there when it started.
This particular scenario started out with fat and sodium hydroxide (lye).
And then, suddenly, POOF ! Soap and glycerin showed up. Where did
THOSE come from ? They came from the molecules in fat and lye,
getting broken up and recombined to make different substances.
THAT's exactly a chemical change.