"Han ændrer ikke sin livsstil" appears to be a correct sentence -- and yet it includes no på. And what about ændre v. forandre?
You can actually use "på" in this sentence, it's omitted because it's not really necessary. "Han ændrer ikke på sin livsstil".
Not Danish, just Swedish but I would like to use the word "skifte".
"skifte" is used when you're changing diapers or batteries or stuff like that. Not sure if this makes sense