Luck is a locked stat at the moment (and doesnt get referenced in general gameplay at this point anyway... though it's supposed to impact lots of stuff in the future). Lani does get luck boosts, but it only lightly impacts her crit chance.
It is intended to have luck largely impacted only through equipment or temporary boosts (like potions or cooking).
If you'd like to manually alter it (and are on pc), you can open the console (shift + O) and type in: player.luk=50 to get 50 luck for Liam. Or any other number.