How is the poem lady of shallot related to king Arthur?

Sir Lancelot doesn't really do anything in the Lady of Shallot: he passes by the Lady's window, and she sees him passing by:- that's it.

The whole point of The Lady of Shallott is that nothing happens in it. Nothing ever happens in Shallott - that is why the Lady is so poisonously bored:

"I am half-sick of shadows," said

The Lady of Shallott.

So Sir Lancelot is not chivalrous, nor unchivalrous: nothing is real inside the four grey walls and four grey towers: it is a limbo, with no opportunity for human qualities of any kind.