The word "lemme" translates to the phrase "let me." The term "feel" means "have." The word "george" is symbolic for a dollar bill. So, the whole phrase translates into "Let me have a dollar bill" and is used when asking someone for a dollar.
Antwayne: You got enough dough ta buy dat cheeseburger off dat dolla menu?
Demetrius: Nah nigga, lemme feel a george.