In descending order, I suggest the following obstacles stand in the way of Celtics win trade for Davis this summer:
1. Kyrie signs elsewhere. (no way we trade for AD in this case).
2. Celtics win the NBA championship. (unlikely, but IF we can make it to the finals, it should be competitive with the Warriors).
3. Another team other than the Lakers makes a more attractive offer.
4. The Lakers make a more attractive offer, that NO cannot refuse.
5. AD changes his mind, and withdraws his trade demand. (Highly unlikely,but they have played better of late, and not impossible to imagine).
Items 1 and 2 are circumstances that we can't control, so put those aside, let's say Kyrie does re-sign, but we don't win the championship this season, or even make the finals. Who is our biggest competition in a trade with the Pelicans?
NY Knicks? Only if they they get #1 Pick, maybe if they get #2 pick, although I doubt the #2 pick has the same cache as Tatum as centerpiece.
Raptors? If they don't win it all this year, but Kawhi decides to stay, I could see them packaging Siakam in a trade that would appeal to NO. Their GM is very aggressive, win now mode. If they win it all this year, or if Kawhi walks, I don't see them getting involved in trading for Davis. Trouble for them is, the likelihood of Kawhi staying there is probably tied to them winning it all, so this would seem to diminish their chances of getting involved in Davis trade.
Lakers? Their major leverage is the knowledge that Davis is very likely to extend there, and threaten not to extend anywhere else. This gives them freedom to offer more assets, because the return would be higher to them than anyone else. Their biggest obstacle is the bad will that has been engendered by Davis agent in conjunction with Laker management, or so it would appear. I don't think the difference in available players between the Celtics and Lakers is meaningful (a case could be made that Ingram has out peformed Tatum this season), and would bet the Lakers are more willing to offer all their top young players than the Celtics. The draft pick advantage of the Celtics really boils down to the potential value of the Memphis pick, which is very difficult to gauge.
Curious what your thoughts on this are, including what other teams do you feel have strong assets to negotiate a trade for Davis. I don't consider Clippers a strong competitor because they lack the player assets.