"She wiped his dry lips with water."
Translation:Ŝi viŝis liajn sekajn lipojn per akvo.
It's true that Esperanto will often use an adverb where English will use a prepositional phrase, but it doesn't quite work in this case. My gut feeling (as a "veteran Esperanto speaker") is that the reason is that "akve" is too vague. Does it mean "with water", does it mean "in water", does it mean "in a watery way"? It's best to specify (using per) that it's by means of water.
I'm trying to come up with a rule for when we use "kun" vs. "per". Is it correct to say that kun is used when you are talking about multiple individuals doing something together, and per is used to describe the usage of some related thing? eg "wiping with water" or "wiping with a towel"