"thick lips" is correct and usable in written English.
You could use it to convey something about the physical appearance of a character in a story, such as "He had thick lips and a wide smile."
His thick lips part, revealing large, square teeth.
Estefano had thick lips and curly, wiry hair.
He had thick lips, and black shoulders, and he moved with unusual elegance.
The thick lips he had as a child were thinner, too.
"I do know," Jeb said gravely, his thick lips trembling in false sympathy.
The puffed-out cheeks, the thick lips and globular eyes make it a perfect three-dimensional cartoon.
The brand changes designs and inventory monthly, and its latest fashion film (the sixth) features Bosworth paying homage to the 1920s screen legend Louise Brooks — replete with black bob and thick lip — while sporting delicate baubles.
Now. the morning after, sitting in the beautiful belle époque Café Glacier Remor with thick lip, sore nose and a bellyful of fondue, I'm definitely looking forward to getting back to Germany.
"I was really worried because my wife had said to me, please don't go on any more pickets, so I was trying to work out how I was going to explain to her what I was doing because of this great thick lip where this chap had smacked me in the mouth.
He is fine though - barring a thick lip - and will be back on.
Sneak in hydration while you sleep: "Gently exfoliate with your toothbrush and apply a thick lip moisturizer," says Dr. Tanzi.
