You know, it's starting to feel like this scenario might actually not happen.
According to Windhorst, Lebron is likely not going to drag this and could make a decision by July 3 or July 4 (FIREWORKS!)
So the Lakers might feel pressured to trade for Kawhi before or around then, but the Spurs and Pop may be in no "big rush" to trade Kawhi to LAL (lol). In that case, Lebron may decide to stay in CLE or go elsewhere (makes that decision sometime first week of July), and suddenly the Lakers might be back to just going hard after PG13 and not being able to add another piece. It's possible George goes to LAL and that is enough to entice Lebron to go there too, but the chances are lower than if Kawhi was traded there beforehand.
And I'm sure even if the Spurs kept Kawhi but then decided to trade him a little later, teams like the Clippers, Sixers or Knicks would still be interested in Kawhi well into July and make an offer, whereas LAL might not bother after seeing Lebron stay or go somewhere besides LAL. Or maybe they still try going after Kawhi (after signing PG13), but it'll still cost them quite a bit.