When you make an ability check, an attack roll, or a saving throw and have disadvantage, you can spend 2 ki points to cancel the disadvantage for that roll.
[...] When a creature makes an attack roll against you, you can use your reaction to impose disadvantage on that roll [...]
Both of these happen "when a creature makes an attack roll", though Entropic Ward requires a reaction, which might be relevant. I'm confused as to the timing of these events, though Xanathar's Guide to Everything does have this section on "Simultaneous Effects" (p. 77):
If two or more things happen at the same time on a character or monster’s turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character’s turn, the player decides which of the two effects happens first.
We also know that both of these features occur before the roll. This is intuitive, as it would be weird to give somebody disadvantage after they rolled (what would even happen if you already rolled with advantage and somebody then gave you disadvantage?). We also know this because there are features which explicitly say they can be used after a roll (such as the Bard's Cutting Words), which these features do not:
When a creature that you can see within 60 feet of you makes an attack roll [...] you can use your reaction to expend one of your uses of Bardic Inspiration [...] You can choose to use this feature after the creature makes its roll, but before the DM determines whether the attack roll or ability check succeeds or fails [...]
So what happens when a Drunken Master monk attacks a Great Old One warlock and the Warlock uses Entropic Ward - can the Monk then use Drunkard's Luck?
What happens if the Monk has disadvantage and attacks the Warlock - does Drunkard's Luck apply first and remove the regular disadvantage, but then Entropic Ward adds a new instance that isn't removed? Does Entropic Ward apply first, and then Drunkard's Luck removes both instances/causes of disadvantage?