To illustrate how this would work in the Celtics' favor, let's say they land the #2 pick and Fultz is already off the board. They aren't particularly enamored with Ball, Jackson, or Tatum, and the cost to trade up to get Fultz at #1 is too steep. So they trade back from #2 into the back half of the lottery and target a big, let's say OG Anunoby or Jonathan Isaac, guys who fit the profile of the modern day NBA big man. The asset they pick up in the process can be packaged along with existing assets to go hard at Paul George, Jimmy Butler, or whomever. Or, you save about $2m off the cap (that's the difference in first-year salary between picks 2 and 8, for instance) which helps you sign someone like Gordon Hayward in free agency without having to trade away key guys in your rotation to fit him under the cap.
I think this is a real possibility and wouldn't at all be shocked if Ainge goes that direction.