What is the theme of the poem? Elaborate

The main theme of this poem is isolation, with its protagonist, Lucy, living alone as the poem’s title suggests, as fair as a star “where there is only one in the sky.” She is so isolated that few people notice when she dies, having lived a life without praise and with few people to love her.
To the poet, however, Lucy’s death is a tragedy, something that will make a great difference to him even if almost nobody else notices any change at all. This brings up a second theme in the poem, one of love and loss, and of the importance one person can have in the world, even if that person seems to have little impact to the casual observer.