Lucky in Waiting For Godot
Lucky is Pozzo's slave. Pozzo has him a rope at all times. Even when Pozzo puts down the rope, Lucky doesn't move or run away. When he's not serving Pozzo, he's standing still while carrying Pozzo's things or sleeping.
The rope tied around Lucky's neck and the way he obeys Pozzo's every command helps establish that he is Pozzo's slave. When he explodes into a speech of gibberish he shows that he does think when he's "not thinking", but isn't educated so there's not much to tell. When he bites Vladimir, it shows that he doesn't take kindly to strangers, or people. It also shows that he doesn't have a lot of manners.
The way he slobbers and sleeps when he's not told what to do shows that he lives only for his master and doesn't have a life of his own to think about. The way he dances, how he thinks he's trapped in a net, shows that he's not free. He's an existentialist caught in the net of life. He doesn't look Pozzo in the eyes unless Pozzo speaks to him directly and tells him to. That shows that he is scared of Pozzo and doesn't want Pozzo to think that he's over-defying him by doing so.
Actions are louder than words
Lucky almost never talks in the play. One of the two times he does, he talks for a while. After they put his hat back on his head, they told him to think. He makes a long speech in gibberish.
Waiting For Godot - Lucky Speech