Because that was the sentence handed down to the person you're talking about.

Her sentence was life without the possibility of parole. Full stop. Of course our legal system has loads of way to appeal or otherwise change a sentence, so that's what we're hearing about here.

Executing people is generally more expensive than incarcerating them for life. Death row inmates are basically entirely separated from gen-pop, and have their own cells, guards, medical staff, etc. (Almost) Everyone on death row appeals the hell out of their death sentence, which usually ends up costing the state a lot more in the long run in terms of court fees.

Also, NH no longer has the death penalty, so if they wanted to retry and execute her (would never happen) I don't think they even could.

Also, this case is/was a national spectacle. All eyes were on the prosecutors and they must have decided that life without parole was a better optic than the death sentence.