Yes, the question does specify a "death penalty" rather than the option to take one's own life. It seems that a prison would need to deny prisoners the means to kill themselves in order to keep those same implements from being turned on other inmates and prison staff.

In the past, some convicted felons have been given the choice of military service or prison, so the idea of letting people chose their punishment does not seem to be antithetical to our system of corrections.

In this case, however, I think a prisoner, regardless of his sentence, who wishes to commit suicide should be isolated, handed a lethal dose of medication and be given an ample period of time in which to marshal the will to swallow it. I don't think they should be forcibly executed even if they say it's what they want.