Death penalty and justice

In the comments on my post about a possible death penalty moratorium in Tennessee, DutchMaus said

I wonder if the concept of justice in many Americans' minds must always involve death. .... no state should be killing its citizens.

Following along with that thought, the Dallas paper had a story about the 3 death penalty cases that the Supremes overturned the other day.

Even so, Texas Solicitor General Ted Cruz, who argued the cases, lamented the decisions. He said in a prepared statement that state and federal appeals courts had struggled for years with the Supreme Court's "rapidly changing and sometimes inconsistent rulings" in death cases. "Unfortunately, today's 5-4 opinion causes yet another delay for the victims' families, who are still awaiting justice in the wake of these senseless deaths," he said.

Other than the fact that it's not the responsibility of the state to provide justice to the family of crime victims (if somebody steals my brother's car does the state reimburse me for his damages?), it seems that the official position of the State of Texas is that justice is never served until somebody dies.