After some playtesting June 05th, 2018: I can confirm as far as my testing goes that Lucky Charm does INDEED stack.
I have Sebille specced into Lucky charm while my main character with Lucky Charm buffs from random armor pieces loots everything. His Lucky Charm has triggered on its own and Sebille's has triggered at other times. Though I'm not sure if the quality of the item is affected.
This means that for every container, Lucky Charm besides the highest holder, has a chance to trigger Lucky charm twice. Though I'm not sure if I'm imagining it, I noticed Lucky Charm triggers FAR LESS on my MC, both his and hers, compared to only having Sebille loot everything.
Overall I think you want to have all characters with 1 Lucky Charm so you can stack triggers but still have a character spec into it and loot everything. Or have 1 character with 5 lucky charm and everybody else has 4 lucky charm (base).