What did Annabel Lee live only for?

First, remember that this poem is being narrated by Annabel Lee's husband, so what you are really asking is what does the narrator say Annabel Lee lives for.

Annabel's husband claims that she lives only to love him and to be loved by him.

Poe has created this idyllic 'kingdom by the sea' where the two lovers live in blissful and serene happiness until the death of Annabel Lee. He has painted a picture of two people that are madly and deeply in love--this love does not disappear after Annabel's untimely death--the narrator still shows his devotion to her even after she is gone.

In essence, the two lived to be loved and to love each other wholeheartedly.