This isn't a question about what luck does for your character, more what kinds of character builds would have a high luck. It could be argued that a gambler (for example) would have a high luck, but a gambler would also rely on a knowledge of the odds, and their experience. SImilarly a soldier would rely on their training. So what kind of character builds would have a high luck?

I can't think of a profession that requires high luck (other than farmer in a desert environment). A high luck would give any profession an extra edge, but skill will win out in the long run. If you require luck, be prepared to lose hard. Luck would be more of a character "definer" rather than for profession. Is he/she known for being lucky or unlucky? Luck is also for perks like Finesse. So now I will say for profession Luck is good for someone who needs critical hits in combat like a sniper, assassin, or gunfighter. Always good to think while typing. Even if you come off looking confused.