Lets be real...she is beyond broken and also extremely dumb to play against. I know you are not supposed to fight her in her ult but I did it anyway cause the game was won and its beyond ridiculous that a 0 4 Illaoi can trade kills with a 5 1 Jax in a straight 1v1. She needs her base damages nerfed by fair amount.
"I know you are not supposed to but I did anyway"
ok well there's your problem ?????
You know, i'd be arguing against this..
But yesterday when I was playing fiora, against an illaoi, both of us level 8,
I built: 
+
+
Illaoi Built: 
+
+
+
+4
Illaoi's AD was 106 and I was at 105.... I'm a fiora, with an almost finished hydra.. and I have less AD than the tank with more health then me and more poke..
After that I just had the realization how ridiculously overtuned she is.
Looks like the haters came and downvoted your post.
You decided to fight in a stupid way and got Gray Screened, boo hoo ..
Except your logic is still invalid and you still fail at playing against her correctly.
Congratulations, you're fed Jax. You're still not anywhere near tanky. You're only slightly bruiser-ish, if that.
Your fault for fighting in her ultimate with your soul presumably ripped out for double damage.
