I want to be fully clear; I was able to max Luck by level 42. It's my 7th playthrough of Nocturne from the point of view of having played 4 full playthroughs of Nocturne in its PS2 form on my 60 GB PS3 back in the early 2010s and my third playthrough of the PS4 version of the HD Remaster. I had to level up vitality for the hospital to clear the hospital dungeon faster, but after that I only ever increased Luck and relied upon NG+ bonuses of higher level demons to get through the game. So, by level 42, Demi-fiend had a maxed out Luck Stat.