Inside Ulduar, each of the four guardian bosses has a room just off the observation ring overlooking the prison itself. But there's no rooms for Loken or Tyr, at least that are still intact. There is a shattered series of rooms that lead down to the prison that could have once been the domain of Loken or Tyr, but since it's been renamed "The Descent into Madness" we may never know.
But anyway, Valnoth implied that the descent might have once been Tyr's station within Ulduar, before the mess with Yogg and Loken really got going, where he served as a sort of final jailer. But where did he go? Maybe Vezax ate him. Or...[maybe he is Vezax].
So while this would answer the lingering lore question of where did Tyr go, it does open a bigger question: if Vezax is actually a corrupted Tyr, why is there no hint of this in the in game lore? Vezax doesn't really have much lore of his own, I had thought of him as just the general of the faceless ones, as implied by the name. But if he really is something more lore-wise, that lore should really be in the game somewhere. Maybe there could have been something in his dialogue, or in the other keepers dialogue, or an thing in the archivum about him somewhere. Or even a questline where you search his temple for clues to where he is, and it's ultimately hinted that he's still in ulduar somwhere, but not quite himself anymore.
Of course, it's also entirely possible that Valnoth is just messing with us, and Tyr will make his triumphant return as a friend/foe in Uldum.