Alcohol containing mouth washes especially listerine, I have a misconception that alcohol is antibacterial and fungus may thrive on alcohol!
I am not so particular about mouthwashes, But keep testing them in trial and error fashion until you find the one which could effectively reduce the white coating on tongue if any and as soon as the local flora is in control you can feel the lips natually hydrate themselves.
I strongly think that a thin candidal biofilm is spread all across the oral mucosa including on teeth, gums, teeth. Its not just candida on lips, its on the entire oral mucosa.