If we had to sum up "Lady Lazarus" in just one word, what do you think we'd say? The speaker is obsessed with death, both literal and figurative. She's attempted to commit suicide in the past, and she keeps playing out scenarios in her mind in which she's a victim of the Holocaust. Lady Lazarus is not in a good mental place in the poem, that's for sure.
In "Lady Lazarus," Plath portrays suicide as a powerful means for taking control over one's life, which makes it a bit less of a bummer.
In "Lady Lazarus," death comes at the hands of others, and represents yet another way in which the speaker has absolutely no power in her life.