”Where I lived" is the place you resided.
Toronto is where I lived [when I was a child] but now I live in London.
Where I lived was a small town and everybody knew each other.
"What I lived for" is what made you happy, what you did or thought about all the time.
I live for playing the piano. I practise every day.
Good parents live for their children.
I hope that's not too bad of an explanation!