now if the guilty murderer is sent to death then the guilty murderer may not suffer mentally if he/she are sent to life in prison.
A guilty murderer who is sent to life in prison might also kill a guard or more in the prison. So even when the guilty murderer is there in prison is in prison the probability of killing others is there in the prison, so sending the guilty murderer to death makes the probability of killing is zero.
Now let's have an example assume that the guard is a pragnant woman in the first two months, a guilty murderer who is sent to life in prison might kill this woman, then two lives will be lost, sending the guilty murderer to death will save two lives if things go well.