One helpful way of beginning to analyse this poem is by noticing the central division that Tennyson creates. In this unforgettable poem by Tennyson the central contrast of the poem is between the world of shadows of the Lady of Shallot and the world of colours of Sir Lancelot. There exist many examples of irony in the poem, which are well worth analysing in order to think about what Tennyson is trying to say.
At the end of the poem it is ironic that it is only when she sings her last song that she is heard by more than a handful of men, and likewise it is only in her death that the beauty is recognised of a lady who had "no loyal night and true." Despite this, she remains an object of mystery and even fear, and the reader is left wondering if anyone understands her character and her death at the end of the poem.
In her choice to embrace life, she has also embraced what comes with life - death. However, ironically, death seems to preserve her character and beauty forever more in a way that would not have occurred had she remained in her tower.
However, by leaving her tower, she has ultimately replaced one uncomprehending picture of herself ("The fairy/Lady of Shallot") with another, and if we see one of the themes of the poem as being about the Victorians' idealisation of women, we are left unsure whether Tennyson is celebrating this idealisation or criticising it. Thus the poem discusses the distinction between "Art" and "Life", and we can see through his poem that he is pointing towards the potential tragedy if "Art" tries to enter into the realms of reality.