When a divination wizard character uses their Portent ability:
Starting at 2nd level when you choose this school, glimpses of the
future begin to press in on your awareness. When you finish a long
rest, roll two d20s and record the numbers rolled. You can replace any
attack roll, saving throw, or ability check made by you or a creature
that you can see with one of these foretelling rolls. You must choose
to do so before the roll, and you can replace a roll in this way only
once per turn.
… to replace a roll, can a player with the Lucky Feat:
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 can choose
to spend one of your luck points after you roll the die, but before
the outcome is determined. You choose which of the d20s is used for
the attack roll, ability check, or saving throw.You can also spend one luck point when an attack roll is made against
you. Roll a d20, and then choose whether the attack uses the attackers
roll or yours.If more than one creature spends a luck point to influence the outcome
of a roll, the points cancel each other out; no additional dice are
rolled.
… use the Luck Roll to replace the result? Or does the Portent trump all rolls and simply give you the final outcome?
This question spun off from discussion on this question.
Some relevant points:
Portent trumps Advantage/Disasgvantage.
Mike Mearls tends to believe that luck can triumph in some cases, but admits this is his opinion, and further seems to conflate the question with Halfling Luck.
I would suggest reading the linked discussion before formulating an answer. There's some good thought there.
Best Answer
Portent overrides Lucky
Lucky allows you to choose which of two dice to use as the roll.
Portent replaces the roll wholesale.
So lucky allows you to choose which toss of the die to use for your roll. Unbenownst to the lucky roller, portent replaces the roll entirely regardless of which die toss was selected as the roll.