Lucky is basically Pozzo’s slave. He is abused physically and verbally, made to work to the point of exhaustion, and denied any opportunity to act of his own accord.
Sounds bad, right? Actually, Lucky’s position is painted as enviable in Waiting for Godot—just consider his name. Sure, you could make the argument that "Lucky" is an ironic term, but it’s also likely that this character really is fortunate—at least compared to everyone else. The fact that the life of a slave is to be desired is a testament to how bad off everyone else is. But it’s also a reminder of the importance of consciousness and certainty—two big problems for Vladimir and Estragon throughout these two acts.
Consciousness and certainty are exactly the reasons Lucky is lucky—he doesn’t have to worry what to do, when to do it, whether he ought to, what the consequence will be, and whether or not he’s happy. He has someone telling him what to do and when. He has in Pozzo much of the certainty Didi and Gogo desire from Godot. He has been saved from responsibility and the agony of choice.
That takes care of the "certainty" bit; the "consciousness" part has to do with the fact that Lucky is fully aware of his position as a slave. Estragon and Vladimir are equally enslaved to their concept of Godot, which is why they "can’t leave," but they believe themselves to be free—they "give [themselves] the illusion that [they] exist." How are they to break the bonds of their servitude if they refuse to even admit such bonds exist? At least Lucky can see the rope around his neck. Vladimir and Estragon can’t.
Still, there are some downsides for Pozzo’s slave (y'think?). First of all, even Lucky can’t be entirely certain that his position as a servant is permanent. At the least, he has to worry that he will lose his occupation (using the term loosely). On top of that is the thought that, if he does have uncertainties, he can’t do anything about it. Lucky can only speak when commanded to—compare his silence to the endless stream of questions coming from Vladimir and Estragon. Lucky can’t ask questions. You could say his suffering is worse because he is forced to do it in silence.
Hmm, it looks like we just argued for his name being ironic after all. Well, there you have it: "Lucky" is both a genuine and ironic term. Look, more duality!
Of course, we can’t talk about Lucky without talking about Lucky’s big speech in Act 1. After all, this is the only time he speaks in the play. At first glance, Lucky is simply piling absurdity on top of absurdity. His speech is full of oddly truncated phrases repeated ad nauseum with no general purpose or design. It’s easy to dismiss these lines as gibberish.
But based on what we’ve seen from Beckett, very little of his play is accidental. We think the speech warranted a closer look, so we went diving in this heap of words and came back with this metaphor. See if you agree:
Given the existence as uttered forth in the public works of Puncher and Wattmann of a personal God quaquaquaqua with white beard quaquaquaqua outside time without extension who from the heights of divine apathia divine athambia divine aphasia loves us dearly with some exceptions for reasons unknown but time will tell […]. (1.639)
First of all, look at the seemingly random phrases that Lucky chooses to repeat: "for reasons unknown" crops up ten times, "time will tell" is repeated four times, and we get four renditions of "what is more." You’ve also got a fair sprinkling of "the facts are these," "beyond a doubt," and "I resume."
We don’t know about you, but we see themes of time, perpetuity, uncertainty, and false imitations of truth—not to mention the overarching idea of repetition and banality. And in fact, we claim in Godot’s character analysis that Lucky draws one of the most profound and vital conclusions in all of Waiting for Godot during this very speech. But that’s another story.
But there’s more. That Lucky uses such academic jargon is a lesson in artifice and deception; he sounds authoritative and intelligent, but in fact lacks any actual substance underneath. Now to us this comes across as a critique of "ivory-tower b.s.," meaning that Beckett is poking fun at the academic jargon used by a lot of intellectuals (who live in an "ivory tower"). This speech is potentially a great explanation for why Waiting for Godot takes the form of a dramatic work rather than a philosophical treatise.