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.
That a maiden there lived whom you may know
By the name of Annabel Lee;
And this maiden she lived with no other thought
Than to love and be loved by me.
There you have it. Stanza one. Annabel Lee lived only to "love and be loved by" the poem's speaker.
Not a lot more to say.