A 14th level Monk has a Diamond Soul.
Whenever you make a saving throw and fail, you can spend 1 ki point to reroll it and take the second result.
A 9th level Fighter has Indomitable.
You can reroll a saving throw that you fail. If you do so, you must use the new roll.
The Lucky feat states that:
You have 3 luck points. 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.
So, if a Fighter or a Monk re-rolls their Saving Throw, does that mean they cannot then use Lucky? Or is the wording just meant to say you don't pick one of the 2 values, but instead just the new one?
As an example:
Fighter rolls a WIS Throw, rolls 1 and DM informs him he failed the save. Fighter uses Indomitable and rerolls, getting a 10. Before the DM tells him whether he succeeded or not, can the Fighter decide to roll an additional Luck die, or must he take that 2nd Indomitable roll?