Level 1 gives precious items (stuff worth a lot), and level 2+ in it gives you a chance for magic items, level 4+ rares, and level 5+ a small chance for legendaries. And in fact, magic+ armor and weapons are the only things you'll find with lucky charm starting with lucky charm 3. (Unless they changed any of these things in the latest patch, not sure).
It's probably not worth it for just act 1, but throughout the whole game it might. The other civic skills are probably better investments mostly, especially barter if you want items. Moreover, it can get inconvenient to have a designated looter and always feel compelled to loot with that character. Probably too obnoxious to try and switch +lucky charm items for looting.
Would be way more convenient to eliminate lucky charm on items and the luck apply to any character within 25m or so of your lucky charm party member. Also feels weird that it doesn't proc off of corpses, either from direct kills or even corpses you find. That would up its usefulness a lot (probably adding 30-50% more times it could proc).
