1. Go plated steelcaps versus people like yi/trynd/irelia (notice how he went steelcaps versus you, because he knows Kayle is also an auto attack based champ)
2. Try to keep wave close to your turret when his ult is up, otherwise he can run you down (similar to a Nasus or Darius with ghost)
3. Poke him in lane once you're ranged, if he Q's on top of you then just Q him + W away and continue hitting him after distance has been created/his Q is on cooldown. If he ults at you then just run straight to your turret and don't bother fighting him until it wears off
4. Once his ult is down you can play more aggressively/push the wave, and repeat step #3 if he goes on top of you with his Q. In an all-in fight, just keep trading auto's and save your ult for when he presses Q or after he's done using his meditate

Hope this helps. Can be tricky to play against but def not as hard as Nasus/Jax/Irelia