Well, I would just take Pedro Alonzo Lopez as an example

By far one of the most prolific serial killers of all time, the “Monster of the Andes” butchered enough people to fill a small town. After killing around 100 tribal women in Peru in the 1970s, he was apprehended by tribal forces that were just about ready to execute him when they were convinced by an American missionary that was staying with them at the time to take him to the police force instead. Unfortunately, the police then just let him go, after which Lopez travelled to Ecuador, where he proceeded to kill about 3-4 girls a week, claiming that girls in Ecuador were “more gentle and trusting, more innocent”. This carried on until he was caught in 1980, but police were still unsure as to his guilt, but a flash flood uncovered a mass grave that had hidden many of his victims, which then led to his arrest. However, the Ecuador government then released him in 1998, deporting him to Columbia. Lopez allegedly said that he was being released for “good behavior”. [emphasis mine]

In this specific example, had they been allowed to kill him, they would have saved 200+ lives. Life sentences are not always for life. A monster like this might even kill someone in prison who had a chance to be reformed. It isn't about vengeance or blood lust, it is about efficacy.

Now if you made the argument that life sentences are cheaper than all of the appeals that death row convicts get to make at state expense... I would tend to agree that the death penalty, at least in the American system, doesn't make fiscal sense. But speaking in a larger context, there are monsters out there that need to be put down.