Background
Luck amulets are said to increase the wearer's luck; wherever this is true or not varies greatly. However if there's no more reliable artifacts available, than it can't hurt to be wearing one of these; maybe it will save your life?
Location
There are 2 good luck charms available at the start of the game; The Golden Lighter also counts as one.
Gameplay
Luck artifacts have a very minor effect on the random chance of enemies shooting at you and also dropping health items when you are low. They also have a very minor chance (about 2 in 255) of completely negating the damage from an attack if it hits. Whilst both abilities are very minor and rare, they're still good to have if you have no other suitable artifacts to equip a certain character.