The relationship between Pozzo and Lucky in act 1 appears to be along the lines of slave and slave master. Pozzo treats Lucky like he is subhuman, keeping Lucky on a rope as if he is an animal. At one point, Pozzo even refers to Lucky as a “pig.”
Pozzo expects Lucky to follow his commands without hesitation. If Pozzo wants his coat, Lucky has to bring him his coat. If Pozzo wants Lucky to hold his whip, even if Lucky’s hands are full, he must figure out a way to hold his whip (Lucky ends up holding Pozzo’s whip in his mouth).
Sometimes, Pozzo dehumanizes Lucky in other ways. Pozzo not only treats Lucky as a slave who must obey every single one of his orders, but he also views Lucky as a source of entertainment. Pozzo makes Lucky dance and pontificate (“Think!”) for his own amusement and for the pleasure of Vladimir and Estragon.
In act 2, the relationship changes somewhat. Lucky still plays the role of Pozzo’s slave or servant, more or less, yet Pozzo is not as powerful as he was in act 1. Now, Pozzo is blind. His blindness leads to an accident that causes Lucky and Pozzo to fall down. That both have fallen suggests that their relationship is equaling out a bit. The newfound balance in their relationship is further evinced by the fact that both Pozzo and Lucky suffer abuse from Estragon and Vladimir.