Let us just remind ourselves for one minute of the definition of these two terms. Non-fiction is a term relating to literature that is based on real life or real characters that is true and not made up. Fiction, by contrast, features characters and situations that may be based in a real world but which are pure figments of the author's imagination. Though there may be a basis in reality, the author feels free to develop and add details as he or she likes.
When we consider this excellent poem therefore, it is clear that this is an example of fiction. The setting of the poem in Arthurian England is based on myths and legends without any historical accuracy. It is not an account of medieval times in England, it is a made up story featuring made up characters. In spite of this though, it is important to realise how beautiful and powerful this poem is. Just because it is not "true" does not mean it is of incredible literary quality and has something to say to us now.
The Lady of Shallot is definitively fiction. It is based on Arthurian legends(themselves fictitious) and is a ballad.
Tennyson's poem has been critiqued as a sensuous piece of fiction without relevance or meaning. However, this Victorian poet is nto removed from his age. His ballad is an allegorical representation of the lack of understanding of the sentiments of women in his age.
The poem refers to Sir Lancelot , one of the knights of the famed Round Table who appears to be the temptation fro her to leave her life's work. Ironically, he is unaware that he is the cause of her death. Thus the lady is trapped by an unknown or unwritten curse that keeps her bound or confined within her ivory tower, ignorant of reality.