To give someone lip is to talk back to them, to speak them in a disrespectful manor etc
Generally when someone speaks to someone significantly older then them with a level of disrespect, contempt and/or in a considending tone that shows they have no respect for their elder(s).
No one likes it when someone gives them lip.
To give someone lip is practially begging them to take you over their knee and give you a spanking.
Adult: Please stay off my grass; you're runing it by running all over it.
Kid: *talks back*
Adult: Don't you give me lip boy!
