live for something/someone        
phrasal verb with live verb uk/lɪv/ us/lɪv/
B2 为…而活着
to have something or someone as the most important thing in your life
  She just lives for music. 她就是为音乐而活的。 
 - More examples
 - He lives for his children.
 - They live for dancing.
 - I live for the moments I can be with you.
 - He lives for art.
 - She lives for the weekends.