In many ways, these poems are quite different. Ulysses is written as a dramatic monologue, in which the protagonist  speaks in his own voice, whereas The Lady of Shalott is described in the third person. Ulysses is happily married and wants to leave home to seek the adventure he remembered from the days of his greatness, whereas the lady of Shalott appears to be single and leave to follow Lancelot. Ulysses ends with the protagonist about to set sail; in Lady of Shalott she does set sail and her death and the end of her voyage are described.

On the other hand, both protagonists are restless and find home lacking satisfaction, and yearn to leave the comforts and predictability of their lives for great deeds (or great loves), and both are treated somewhat sympathetically by the poet.

What is the thematic connection between "The Lady of Shalott" and "Ulysses"?

The main thematic connection between the two texts lies in the contrast between the apparently enviable external circumstances of the protagonists and their internal lack of contentment with those circumstances. Ulysses has successfully returned home after his long voyage, is united with Penelope, famous, has a son he can be proud of, and yet is restless because he misses the life of adventure, and wishes to again embark on a voyage to do more heroic deeds.

The Lady of Shalott is wise and beautiful and rich, with many suitors, but because she to is discontent with her circumstances (unrequited love for Sir Lancelot), she also embarks on a boat journey to Camelot.