Hi there, party members cannot be changed while in the dungeon.
Luck stat cannot be increased when levelling, this is intentional.
Luck can be increased by taking cards in the dungeon and will only apply throughout the run of the dungeon.
Other ways of increasing Luck is from equipment / skills.
Luck scales with Critical Chance and vice versa to deal more Critical damage. This only applies when Critical Chance is over 100%.
Hope that helps!