Alright so I've heard talk of specific rules overruling generic rules, but both of these seem like specific rules to me.
So the Halfling racial trait Lucky (which I'll call Halfling Luck from here on out, to help avoid confusion) states:
When you roll a 1 on an attack roll, ability check, or saving throw, you can reroll the die and must use the new roll. (PHB, 28)
and the Lucky feat specifies:
Whenever you make an attack roll, an ability check, or a saving throw, you can spend one luck point to roll an additional d20... You choose which of the d20s is used for the attack roll, ability check, or saving throw. (PHB, 167)
Meaning that if you use a point with an advantage or disadvantage roll, you're allowed to choose from any of the three rolls.
So if you use Halfling Luck to reroll a 1, can you then decide to use a luck point and still get to choose any of the dice? Or if you use a luck point and that dice rolls a 1, do you reroll it with Halfling Luck and then still get to choose any?