Fiora dying during ult w/ 500 HP

Playing Fiora in my last game I was a bit fed (11-5 at the end) i ulted onto the enemy team i hit 3 with my ult (rek'sai, kalista, and leona) but after my first 3 hits I immediately died. They had no thornmail, a single ignite, I had no DoT on me. Ignite at the level of the rek'sai would have done about 300 damage, well under the HP i had going into the ult. I'm just wondering how a fizz trickster can dodge a liss ult after it's been cast, but a fiora can just drop dead from no apparent reason. Shouldn't all the abilities that make you untargetable make you untargetable on a consistent basis?