Yes LUCK and INT would be part of making a Bucket, also probably some other Stats, just those two Stats in particular dont do much, you could be dumb as a Brick but still be a good Blacksmith.
LUCK would only make the difference between 2 levels of Quality at most, so if you make 100 of something, luck determines the rough ratio between good bucket and slightly better bucket, meaning you would if you spammed crafting end up with only 2 different Types of Buckets, that is how minimal the difference is.
You wont get Legendary Items by having Crap Stats but high Luck. You would end up with either a Crappy Bucket that doesn’t even work or a Crappy Bucket that barely works, when it comes to the lowest Tiers.
LUCK basically just gives you randomly a +1 to the output Quality Tier of your Stats with a random Chance, kindof like a Critical Strike Chance for example. So 100%-ing your Luck if it was even possible, would net you just a +1 increase of every other Stat for example.
When unstacking Items the random Item you’ll get could for example be the most “different” one from all other Items if your LUCK is high, so you could get the best Apple or the most rotten Apple with one pick (ofcourse you should still examine it first to see if you got good or rotten in that case).
Edit:
Also the LUCK Stat would be the same for every new Player, so you dont end up scrapping players just because you somehow managed to find out you have a bad LUCK Stat. Another thing I would do is letting the LUCK Stat fluctuate a little, so you have days where you have more LUCK than usual, or worse LUCK.
Edit 2:
Said Stat would also be defaulting to 50% Luck, so it makes more Numerical Sense to have a 50:50 Chance on a Coin Flip.