@Geek of Ages
That's a ridiculous amount of purple prose to avoid a simple sentence. And ultimately give the reader less information—not to mention requiring other context clues.
It's not purple prose. Purple prose is flowery descriptions, like a lot of adjectives. It's showing.
Is she licking her lips to be sensual (since some people apparently find it so—I do not), or because she has dry lips, and the two points are meant to juxtapose against each other? (Assuming the eye-batting is also sensual, instead of her trying to get dust from her eyes)
It was a couple of sentences taken out of the context of the story. Showing isn't replacing one sentence with another. There would be a build-up to this that would let the reader know the intention of her dialogue, eyelashes batting, and licking her lips.
What does the narrator (or, if the narrator is being omniscient-ish, the character whose thoughts are being narrated) think of the event? We don't know. We're left with having to guess at what anyone thinks about the situation.
An omniscient narrator knows all so he could tell what she's thinking. Without that narrator, if the guy is the POV character, he doesn't know what she's thinking. That builds tension in the story. That's a good thing.
You're describing events like a camera, not like a person.
Exactly. That's what showing is all about. When you watch a movie, there's no narrator telling you what you're seeing. The viewer lives the story through the action and dialogue (the camera).