It’s worth noting the contrast between Divine punishment and an earthly court.
It’s brought down that the Beis Din shel Maala only punishes someone once they turn 20.
This is in contrast with the beis din shel matah, which will execute a youth once he is Bar Mitzvah.
The reason is because the Heavenly Court can judge a person’s intent, mental state etc. A person hasn’t fully finished developing until 20 years old; so the Heavenly Court can take those factors into account and delay or mitigate his punishment.
In contrast, a beis din is all about the action. If a person committed an aveirah which carries the death penalty, then (assuming witnesses hasraah etc.) we will kill him based on his actions.
The fact that he struggled maturity wise is irrelevant down here. We need to put an end to these sorts of actions, and the Torah teaches us that the way to “eradicate the evil” is by executing the wicked.
So while we could feel rachmanus for the sort of life the murderer has experienced, we still should execute him. The Rachmanus should not be a factor when establishing him punishment- even though it’s very possible that the Divine Court may take it into account.