Yeah, my first thought was that she's caring for him (and his dry lips) as he's dying. Yes, that makes this sentence kind of depressing.
'Kun' means 'together with' whereas 'per' marks an instrument. They just happen to both translate as 'with' in English, but the meanings are very different.
Kial? I would expect this sentence to be more like "Ŝi viŝis liajn lipojn per malseka tuko."
This sentence makes me think she is holding water and using it to wipe his lips. That's a god-like ability!