"Lady Lazarus" is a poem spoken by—yup, that's right—Lady Lazarus.
Lady Lazarus is a figment of Plath's imagination. There never was a real Lady L, no matter how hard you Google.
But Plath was a smart cookie, and she used the name of her speaker as an allusion to Lazarus (from the Bible). Lazarus is a character from the Gospel of John who died and was resurrected by the one and only Jesus. The Bible doesn't give much detail about exactly what he looks like when he is raised, but the idea of someone who's been dead for four days suddenly coming back to life is kind of creepy and miraculous at the same time—just like it is in this poem, "Lady Lazarus."
And like Lazarus, Lady L experiences death and returns from it, but unlike Lazarus, Lady L accomplishes this feat all on her own. She is in control of her own destiny—even if that destiny is another death. That's a bragging right that the original Lazarus can't claim.
For more on Lady L, check out what we've got to say about her in the "Speaker" section.