If a 13 year old brutally kills another person, then yes, I do think they should face life in prison without parole. This is just how the world is and works as it stands. What are they going to do if and when they get out? Is someone going to give them a job? No.
Yes, a thirteen year old should face life in prison without parole, if they have taken another life. The person who is dead does not care that the person who killed them is only 13. They lost their life. So it stands to reason that the person who took that life should lose their life too.
13 year olds are too young to be held accountable for their entire natural life for any crime they commit, regardless of how heinous it is. If need be, they could be sentenced to mental institutions where their potential release is decided by psychiatrists instead of a parole board, but no kid should ever be locked up forever.
No one should be subjected to life in prison. This is very expensive to taxpayers and provides no benefit. If a violent criminal is so definitively guilty and completely irredeemable, the death penalty should be applied. That said, I don't believe a 13 year old can be determined to be irredeemable. Children's brains are still forming at that age and it is entirely possible that time, training, and medicine could reform a 13 year old. At the very least, the final decision of such a long-term punishment should be withheld until the child has received treatment and reaches at least 18.