It appears that, if you use an ultimate at approximately the moment you die, the ultimate will not show it is on cooldown. Had it happen most recently in a game as Graves, where I used my ultimate to secure a kill at the end of a fight, but died due to Kha'zix jumping me.
(Tentative) Repro. Steps:
1. Enter a game
2. Hit level 6
3. Use ultimate at approximately the moment you die
4. Ultimate does not correctly show that it is on cooldown, but cannot be used until the cooldown time has passed.