Is it necessarily just lethality?
I mean, I see how lethality has become popular followed by ninja tabi.
I don't understand how lethality being strong makes tabi necessary though...
Tabi reduces all damage taken from basic attacks by 12%. Meanwhile, lethality is strongest on AD Casters like Jayce or Varus who can repeatedly send out powerful long range poke from safety and decimate the health bars of squishies before a fight (thereby making it a won fight). Tabi's passive does nothing against that - they're no better than any other 30 armor item in that case. Really, I think tabi are popular because they provide the little bit of armor that's so important against lethality (the first 30 armor against someone with two lethality items completely negates all of their lethality at level 18).
Correct me if I'm wrong, but I believe the formula would work out to:
Let's assume a level 13 Ezreal with 9 armor seals for a total of 69.2 armor, against someone with 7% armor pen and they're not running lethality marks.
No armor built:
100 / (100 + 69.2*0.93 - 30) = takes 74.43% physical damage
Ninja tabi is only armor (30)
100 / (100 + 99.2*0.93 - 30) = takes 61.63% physical damage
Builds a 60 armor item:
100 / (100 + 129.2*0.93 - 30) = takes 52.59% physical damage
Notice how 61.63 / 74.43 = 82.8%, or equivalently that first 30 armor reduced his damage taken by 17.2%.
Now 52.59/61.63 = 85.3%, or equivalently the next 30 armor only further reduced 14.7% of damage taken.
That's 2.5% less effective (or in percentage of the first difference, 14.5%) for the second 30 armor than the first 30 armor.
Basically what I'm saying is, they want to invest in a little armor, but don't want to take away too much of their build to invest in a lot of armor because it has diminishing returns. Ninja tabi allow you to give up VERY little (a bit of Attack Speed that you can get a lot of anyways) in order to get the armor you want for cheap. There is no alternative really - any other armor item is going to set you back over 2K, give you other stats you don't want/need, and take up a full slot of your normal build (i.e. you're giving up on an AS or Lifesteal item).
I don't think ninja tabi is a specialist item against lethality. I think it's an item that allows efficient access to some basic armor that any champion can opt in to, and becomes important when lethality makes AD poke more popular. If anything, Tabi's passive would be much better in a crit-ADC meta where they're actually auto attacking a lot.