Symbolism, Imagery, Allegory
The novel opens with Esther's obsession with a gruesome electrocution, which signals ahead to Esther's experiences with electroshock therapy, and also to her memory of being electrocuted by her father's lamp. The most immediate thought that comes to mind whenever you do see electrocution in the novel is probably just, well, the irony. The scenes where electroshock therapy are described are shocking in and of themselves, and a lot of the novel's material is shocking – Esther's "rehearsals" leading up to her suicide, her violent encounters with Marco and Irwin, just to name a couple of the more gruesome bits. Given all that, it seems pretty ironic that society's cure for someone deemed "shocking" like Esther is … shock. Like, they're going to use the same method they use to execute enemies of the state (the Rosenbergs) on the mentally ill? Whoa. That also brings up the question of the function of the novel's shocking material on the reader. Is the novel supposed to be therapeutic for us in some way?
Now the link up with her father – that's a bit more elusive. Perhaps it has something to do with the fact that Esther feels abandoned by her father, as if her father was somehow punishing her by dying. Or perhaps a broken lamp is just a broken lamp.