You know what might be neat? Maybe you spend Luck to guarantee a hit, but the amount of luck that it costs you is rolled each time? Maybe 1d6?
I love this. I'd even let this be used against being hit, or basically to modify almost any die roll. Yes, you can avoid being hit by the spear trap. Yes, you may be able to avoid dying and only end up spending 1 luck point. But it could cost you over half your luck, or more, and either way, the decision you're making has a potentially steep cost. Obviously, if you run out of luck on the d6 and you end up with 0, you've essentially killed the character anyway. Maybe instead of getting hit by the spear, he has a sudden brain aneurysm and collapses anyway.
I think this gives characters a mechanical agency in their own survival, but comes at such a potentially steep cost that it's not done lightly. I haven't looked super closely at the classes yet, since I'm gearing up to run the Level 0 Funnel thing, but Thief Luck and Halfling Rub Off Luck could just work like normal, adding the +1, unless the Thief wanted to guarantee his success in the same way and roll the d6 to see how much it costs him/her. Or honestly, if the Halfling was willing to take the same chance to guarantee the success of one of his party members, why not let him take it? He's not going to regenerate his luck fast enough to be abusive, unless he consistently rolls low on the d6, in which case, he's getting lucky, and that's fine.
Thinking on my feet here, but what if characters could use luck either way--to get a small +1 bonus to one of their rolls per one point of Luck as per the rules, or risk 1d6 points of luck for a guaranteed success, avoidance of an enemy's attack, or what have you? I agree that players having to decide after each hit might add a little bit of length to the game, but it seems like a potentially rewarding decision point and would only be used when the character was fairly certain that the hit would kill them, leading to a d6 roll with a lot of consequence and attendant drama, especially if the character's luck is 6 or less.
Anyway, as others have said, unless there's some incentive for burning Luck before the roll, there's no reason anybody would do that, as opposed to after the roll. A flat +2 in addition to +1 per Luck point expended prior to a roll was suggested elsewhere, and that might be enough of an incentive, or possibly too great of one. Even with this, one Luck point before the roll gives a +3, which is fairly significant. Any kind of 2-for-1 deal seems too much, at least to me.
One thing nobody has mentioned is that a character's Luck does play a factor in NPC's attacks against the character, but only when that NPC scores a critical hit, in which case the Luck modifier applies negatively to the NPC's Critical Roll (as I understand it, per page 11 and page 79). This seems a little fiddly and unlikely to affect too much, but maybe that's okay.
As far as characters regaining luck, I don't see this as something that needs rules-mandated at all. The rules seem very clear on it--
"The Luck score changes over the course of a character’s adventures and is linked to their alignment. Characters
that act against their alignment may find themselves suddenly unlucky. Those who swear an oath to a patron of their newly desired alignment may find the change easier....Players would be well advised to understand the goals of gods and demons that shape the world around them, for they are but pawns in a cosmic struggle, and their luck on this mortal plane can be influenced by the eternal conflict that rages around them." (pg 12)
It's easy to imagine a Lucky Boulder held sacred by Chee-Shrekial, the Saint of the Plateaus, where those unlucky in life make risky pilgrimages to offer their prayers, or a ruby amulet worn by followers of Kantixala, a minor Demon of Numbers who looks after his own, or a neglected shrine in a dank ruin that a PC cleans the dust off of, endearing them to some forgotten deity. Some sort of flat "PCs should regain 1-3 points of Luck an adventure" or something cheapens the concept of Luck and seems against the spirit of the game.