lethality garen

I mean, yeah, it's physical damage. All lethality does is reduce the armor of the target you're facing. It's not some special on-hit effect. It worked just as well on the old Garen. And by "just as well", I mean "suboptimally".

Lethality is for bursting down squishy targets in the early game before they have a chance to build armor. Garen doesn't deal good burst, and he generally lanes against other bruisers, tanks, and the occasional ranged top laner. In lanes with actual squishies, he's just going to get kited out for days. That's why assassins build it; they have the mobility to impose their burst on a target.

If you build lethality on Garen, you're E will be doing more damage than baseline, but it won't be doing significantly more damage than if you had taken a different AD item or an AS item, and now you aren't as tanky as you need to be to function.