Retribution is just another word for revenge, and the desire for revenge is one of the lowest human emotions — perhaps sometimes understandable, but not really a rational response to a critical situation. For a Christian, this is an urge to use violence for one’s own purposes, and urge which should be resisted. To kill the person who has killed someone close to you is simply to continue the cycle of violence which ultimately destroys the avenger as well as the offender.
That this execution somehow give 'closure' to a tragedy is a myth. Expressing one’s violence simply reinforces the desire to express it. Just as expressing anger simply makes us more angry. It does not drain away. It contaminates the otherwise good will which any human being needs to progress in love and understanding.