From Backpack Hero's Discord FAQ:
Q: How does luck work?
A: Every time an item is discovered (including "reorganize now" items), a random number is chosen. The higher the number, the better the rarity. When you find an item, other item rarities become likely to be found. So if I find an uncommon item, rare and legendary items become more likely. Once I find an item of a certain rarity, my luck for that rarity is reset to 0 and I need to rebuild luck for that rarity. Getting "luck" from an item, increases your chances for all rarity types.