Boethiah's sphere is "deceit and conspiracy... treason, and unlawful overthrow of authority," which sums up rather nicely the Aldmer view of Lorkhan as a trickster and betrayer, as well as the mythic role of the Rebel in general.
One can also make the argument that Boethiah is a god of ambition and mortal undertaking, given that On Oblivion notes that she "inspires the arms of mortal warriors," as well as this gem from Boethiah's Proving: "I am alive because that one is dead. I exist because I have the will to do so. And I shall remain as long as there are signs of my handwork, such as the blood dripping from this blade."
Both use a serpent as one of their symbols (Shor's totem animal is the snake, Boethiah's realm is known alternately as Attribution's Share or Snake Mount, and her statue in Skyrim has her draqed in serpent's tails).
And, Boethiah was the original god-ancestor of the Chimer, who convinced the prophet Veloth to lead his people east to Morrowind, where the Heart of Lorkhan lay waiting for the Tribunal.
It just seems like an awful lot to just be a coincidence. Could Boethiah perhaps be a fragment or shadow of Lorkhan, or maybe a leftover from a kalpa where Lorkhan didn't participate in creation?