"Lady Lazarus" is an undeniably violent poem. It's filled with mangled bodies, fierce circus crowds, and murderous Nazis. The best way that Lady Lazarus (and, for that matter, Sylvia Plath) can communicate her deep depression to us is through violent imagery and imagined experiences. We don't know much about Lady L's life outside of the poem, but her imagined life of brutal circuses and concentration camps is a violent, horrific place. We don't want to go to there.
The violent Holocaust imagery in the poem is a powerful way for Plath to express her emotions, and she has every right to use it.
The violent Holocaust imagery in the poem diminishes Plath's emotions, because the suffering of one woman could never equal the deaths of six million Jews.