He has been better, but I think Rhaast is still super strong with the right items.

Lethality is armour penetration. AD is... AD

AD increase your damage with auto attacks and some abilities (in Kayn's case, all of his abilities). Lethality ignores armour based on your current level and how much lethality you have. At level 18 it's a 1-1 ratio (so 20 lethality is 20 armour penetration).

It scales super well with Kayn because he is an ability based slayer. Slayers are either Assassins or Skirmishers (Kayn is both). Full assassins are champions like Talon, Zed, Kha'Zix and Ekko. Skirmishers are like Yasuo, Master Yi and Fiora.

The assassins do high amounts of damage in short windows usually with mobility (blinks, dashes and speed ups) to kill a low hp/armour target as fast as possible (mages, ADCs and other assassins) whereas skirmshers are basically melee ADCs.

Lethality scales incredibly well with itself (the more lethality you have, the more armour you penetrate so the more you add the more you pen etc etc). Most abilities (Including Kayn's) do not scale off of critical strike. Crits are soley on basic attacks and specific attacks ( Alpha Strike, Parrrley and Steel Tempest are the most prominent melee critical strike abilities). Kayn has none.

So Kayn wants Lethality, Attack Damage (AD), Cooldown Reduction (CDR) and some defence (such as health from Black Cleaver or resistances from Ninja Tabi. As he deals most of his damage from abilities, and he has no ability that scales with critical strikes that leaves flat AD items and lethality based AD items (such as Death's Dance, Enchantment: Warrior, Youmuu's Ghostblade and Edge of Night.

TLDR: Lethality is a bonus stat on a lot of AD items so they're automatically bought together. Lethality is armour penetration and armour pen on a physical damage champion is always good, especially when they deal most of their damage through abilities in burst windows.