I remember reading somewhere on the Wiki that on tier 1 enemies only do normal damage, while on tier 2 they do half & half. But I can't find it anymore, is that correct? So there's no use equipping armor against piercing/elemental/shadow while on tier 1?
Related: on T1 lockdown, is it useful to equip piercing armor or is damage type limited there as well?
Yes. It's true.
LD damage is exactly what damage the weapon used is