The poems are all different, different variations. Speculation about who Lucy is goes from his sister Dorothy, Mary Hutchinson, or a made up person - who may or may not be a conglomeration of people Wordsworth knew (possibly including those mentioned) as well as his own idealizations.
Themes, Mood and Inspiration:
The poems are about a muse: love, or object of affection, inspiration - loved from afar and the poet's/speaker dealing with the death of that person (Lucy). Compounding that grief is that Lucy was the inspiration for the poet's creativity. So, the mood is elegiac, melancholy. Other themes and moods are nostalgia, imagination and memory which dominate a lot of Wordsworth's poetry.
The Lucy poems begin with "Strange Fits of Passion Have I Known." This speculates about the death/disappearance of his inspiration with the sinking moon analogy. The speaker reflects on what his mood would be like in the wake of the death of his ideal love.
"She Dwelt Among the Untrodden Ways" - Lucy's isolation and being relatively unknown until news of her death. Imagine reading a gravestone of a person unknown to you and imagining/creating idealizations of what that person may have been like.
"I Traveled among Unknown Men" - probably praise for Wordsworth's native England, with the comparison between Lucy and the natural English landscape.
"Three years she grew in sun and shower" - again, linking Lucy to nature; her death separates her from nature and humanity.
"A Slumber did my spirit steal" - the finality of Lucy's death and the speaker's calm because Lucy is at peace and beyond the trials of life. There is almost a consolation for the speaker because although Lucy has died (as if in a dream - 1st stanza and then in reality - 2nd stanza), she is now more connected to nature, albeit separated from humanity.