When I'm using a character with a shielding ability such as Lee Sin's Iron Will, does the "power" of the shield factor in the defenses of the champion? For example, does the 200 armor Malphite's shield last longer than an AD carry's shield?
Shields (or more formally, absorption shields) provide temporary health to a champion which is capable of mitigating damage dealt, sometimes granting an additional bonus effect as well. Since they act as extra health, they are affected by the champion's resistances.
So yes, assuming both shields are entirely depleted, a shield on a 200 armor Malphite will last longer than a shield on a 90 armour ADC.
Through some rudimentary testing, Barrier (as expected) also takes armor and magic resist into account.