Lucky Break will trigger even if the incoming damage is reduced to 0.
Besides perks that have group effects, perks can be selected to be shared among team members. Each player can only choose one perk to be shared at a time, and the selected perk can be changed at any time during gameplay. However, the player must have a Charisma point level that is at least three times the rank of the perk card that is to be shared, regardless of what SPECIAL attribute the shared perk card belongs to. Shared perk cards will not stack effects if duplicates are equipped or shared.