The luck increases as you find clovers. There are only 2 of them, in the park and in the mall. Therefore, the maximum luck is 2. It is not used anywhere except for the mini-game on the main character's computer.
Requirements for Ash's Level 3 event: "You have to complete the major event of the Second Act. Also, your stats, EXCEPT for luck, must be >= 10." So, only Strength, Agility, and Endurance must be greater than 10.
