"Τα κόκκινα χείλη."

[carmina_banana]

does this word have a singular form?

[D_..]

Yes, χείλος, and it is used either in anatomy or metaphorically to denote 'edge' e.g. το χείλος του γκρεμού = the edge of the cliff. For more examples see here.

[HellasCad]

Yes, it would be "το κόκκινο χείλος".