I mean, dont expect to do anything against Kayn if youre support. Depending on what support you are playing, only thing you can do is CC him or protect yourself with a shield or something. Everything else relies on your team on actually killing him. Main reason why I dont enjoy support anymore.
#What do you build against lethality kayn
granite chasm
There is no such thing as a good support item to stop Kayn in what he is doing, if he is fed, the only item that will save you is Hourglass. If you really need it, then go for it, because chances are your team helping you is little to none. But I suggest just stick to the normal build path of whatever champion you are playing, tell your friend to peel for you if Kayn goes for you and vice versa.
ADC/Support can easily win a Fed kayn if you guys play it well
"What do you build against lethality kayn?"
Lethality is only good against low armored targets, so the best way to build around him is obviously Armor. There are a bunch of no brainer armor items that are really good for AD champions such as Death Dance, Thornmail, Deadmans Plate, etc. What you should have against every Kayn if you arent playing support is always Death Dance. Since blue Kayn is a burst type champion, having Death Dance will basically make his damage dealt to you less.
quartz creek
Lethality kayn is an assassin-burst build, so squishes should stay away from him to mitigate his win con. If you want to fight him as a squishy, land your cc and burst then run.
safe goblet
armor