This is my attempt at adapting Luck from TOV with Heroic Inspiration and the Lucky Feat:

You start an adventuring session with 0 Luck, losing any Luck you had left since the last game*. You can use a d6 to count your Luck points at the game table.
(* For a character with the Lucky feat, see below.)

Gaining Luck

• Once per turn, when you fail to hit with an attack roll or fail a save, gain 1 Luck.
• The DM can award 1 Luck as a reward for a clever idea, excellent roleplaying, or pursuing an interesting choice that isn't optimal.
• The DM can award any amount of Luck to one or more PCs for achieving certain goals.

Losing Luck

You can have a maximum of 5 Luck at one time. If you already have 5 Luck and gain more, you must immediately roll 1d4 and reset your Luck total to the number rolled.

Spending Luck

• Spend Luck to add a 1-for-1 bonus to a d20 Test. Example: you roll a 13 on a d20 die; you can spend 2 Luck to make the result 15.
• Spend 3 Luck to reroll the d20 after a failed d20 Test. You must use the new die result.
• Spend 2 Luck to reroll the damage dice of an underwhelming Critical Hit.
• Spend 1 Luck to reroll a single damage die.  

Note: Luck can't stop a critical miss on a natural 1 or create a Critical Hit by adding up to 20. Luck gained from a failed attack or save can't be used to enhance the same roll that generated the Luck. It can only be used for a future d20 Test. 

Lucky feat

If you have the Lucky feat, you start the adventuring session with a number of Luck equal to your Proficiency Bonus. After a Long Rest, you start the day with your current number of Luck or Luck equal to your Proficiency Bonus, whichever is higher.

The Luck feat grants two other ways of spending Luck:

• Immediately after you roll a d20 Test, you can spend 1 Luck to give yourself Advantage on the roll.
• When a creature rolls a d20 for an attack roll against you, you can spend 1 Luck to impose Disadvantage on that roll.

You can spend Luck for the Lucky feat benefits a number of times equal to your Proficiency Bonus and regain the ability to do so after a Long Rest.