The speaker of "Lady Lazarus" is Lady Lazarus herself, and in that sense, this poem almost reads like a monologue. Here's the lowdown on the star of our show:
(1) She's extremely depressed, disturbed, and suicidal.
(2) Her name references the figure of Lazarus from the Bible—a guy who died and was resurrected by Jesus. But there's no Lady L in the Bible; our Lady is Plath's creation.
(3) Lady L is a whole lot like Sylvia Plath, who committed suicide not long after writing the poem by sticking her head in a gas oven.
(4) Despite her similarities to Plath, it's important to remember that poems are not real life, and that Plath has gone out of her way in this poem to speak in the voice of Lady Lazarus—not in her own voice. Thus, it's key that we talk about Lady Lazarus when we discuss this poem, not Plath. While the poem may give us a tiny little window into Plath's feelings, we can't assume that we know her just because we've read one of her poems. Or that we know Lady L, just because we've got a bit of Plath's autobiography under our belts.
(5) Lady Lazarus is one powerful lady. Despite all of her suffering, she seems to have serious control over the one thing that matters most to her—her language. She may often feel like a victim, but her words have serious bits. She ends the poem by "eat[ing] men like air." Go get 'em, Lady L.