Prison suicide rate is 10.4 to 18 per 100,000 inmates depending on whose estimates you trust and what year you use. Suicide rate in the US population is 12.6 per 100,000. Most of the suicides are
not among lifers. That suggests the prisoners kill themselves at almost the ordinary rate, for the usual reasons, and has nothing to do with them serving life.
If you've ever actually talked to corrections people, they'll tell you that the lifers claim that they'd "prefer" the death penalty is typical of the con jobs they're constantly trying to pull.