So you're taking about 25% of the physical damage he would be dealing . (45% reduction on bonus armor from LDR, 7% pen from battering blows)
Before reduction:
does 4% max health per auto. you had 4047, which comes out to 162 per auto.
does 8% current health per auto. The damage dealt goes down as your health drops, Just average it at 162 per auto. Also if he used the active, that's another 404 damage
does 15 magic damage every attack, and every other attack applies on hit effects again.
does an extra 15% damage
Red buff burns for 38 true damage
His E deals 50 + .25AD true damage every hit
Bounty hunter deals an extra 7.5% damage assuming he had 5 stacks
At level 18, yi has 111 base AD, and he had an additional 13 from runes, 48 from fervor, 25 from bork, 53 from rageblade, 50 from ldr, 20 from hexdrinker, and +10% bonus ad from his E passive, totaling 341 AD, meaning his E is dealing 135 true damage every auto.
So without any reduction, that would be 1036 damage every auto, and 1375 damage every other auto, 173 of which is true damage.
With reduction, that's approximately 389 every auto, and 473 every other auto. It would be higher at the beginning of the fight and lower at the end because of the variance in damage from bork, but that's average. If he used bork's active, that would have dealt about 100 damage.
The fight lasted just under 4 seconds, and Yi had capped attack speed, meaning he would have done 9-10 autos + alpha strike + bork + red buff burn. Average it to about 430 damage per auto.
That's why you died.