I believe, from having studied decompiled Wizardry 1/3 source that:
* Each character has saving throws for different categories; the base value of these saves are based off the character's race.
* Every certain number of levels (think it's either 3 or 5) improves your saving throws by one point; hence, at extremely high levels, this no longer matters.
* Luck further provides a bonus to saving throws.
* Saving throws apply mainly to certain attack types (for example, a Priest's saving throw determines wither they are petrified by Priest Blaster traps or just paralyzed), or whether status ailments from enemy physical attacks are applied (this includes level drain, I believe).
* Luck only protects the character with the stat, not the rest of the party. It does not affect the chance of triggering the trap, but might protect the thief (and only the thief) from it; furthermore, it might not protect against all of them. It does not provide any magical protection, not even against spells like Katino.
Anyway, I don't consider Luck to be that important, and if I were to have a lucky character, I would rather have it be a priest than a thief (being able to cure status ailments is more important than being able to disarm chest traps when your party isn't in good shape; treasure hunting can wait). For Thieves, in any case, Agility is far more important (and it's good for offensive casters as well, to nuke enemies before they have a chance to attack).
By the way, which version of Wizardry 5 are you playing?