1.
If you live out your life in a particular place or in particular circumstances, you stay in that place or in those circumstances until the end of your life or until the end of a particular period of your life.
Gein did not stand trial but lived out his days in a mental asylum...
I couldn’t live my life out on tour like he does.
PHRASAL VERB : V P n (not pron) , V n P
2.
If you live out a dream or idea, you do the things that you have thought about.
He began living out his rock ‘n’ roll fantasy during his last year in law school...
I suppose some people create an idea of who they want to be, and then they live it out.
PHRASAL VERB : V P n (not pron) , V n P