In my experimenting I found that lucky charm only benefits that character. So put all your lucky charm gear on one character. It only works on chests, barrels, crates, etc.. As far as I can tell it does not work on kills. (Unless they kill the thing? I didn't check that)
What it does: it's a proc. I don't know the rate per point, however, when it works there is a sound notification and 4 leaf covers fall from above the character. The result is 1-2 extra pieces of gear. I haven't seen any indication that it gives better gear/items, only more items/gear. I could only get to +4 lucky charm because of drops and vendor availability. I did a lot of save scuming (yes it's still possible, just not as easy) to see if it is worth it.
At this time I don't think it is worth putting points into lucky charm. In a single playthrough without save scumming and ending with +3 lucky charm and opening every single container with that character it procd 3 times. Always 1-2 pieces our extra gear/items always common gear not colored. YMMV, I think you are better off with points into thievery/sneaking and taking items off of vendors.
