To give someone some lip means to speak to someone in a way which is rude and doesn't show respect.
That rude young boy gave me some lip when I asked him to stop smoking.
She gave her neighbour some lip because she was in bad mood. Now he wants to move house!
To pay lip service (to something) means to say you support something without really meaning it.
The food industry is only paying lip service to government campaigns to make people eat a healthy diet. Their products are very high in salt and sugar.
Women from the Suri tribe in Ethiopia use clay lip plates. From an early age, they pierce and stretch their lips to accommodate the plates. The size of a woman's plate determines the number of cows her family will receive when she marries.