I don't disagree with either of your assessments re: Lauri and Chicago's position; however, I do disagree with the inference that Lauri's misfit with the Bulls directly means the Spurs would be able to get him via trading DDR to them. I hardly think the Bulls would like a heavy ball-handling guard taking shots away from Lavine (not to mention being unable to space the floor or C&S when Lavine penetrates to dish it out), not to mention DeRoz's no-D, which would be exacerbated on the Bulls, considering both Vuc and Lavine are not exactly lockdown defenders or close to it. Your "Big 3" all being able to get their own shot is great in theory, but teams don't want the kinds of shots DeMar gets, and the time/effort/ball-hogging it takes for him to get them, in the modern game.
I can't say for sure what other packages will be on the table, since many times random teams decide to blow it up or make certain players available after weak/disappointing playoff runs; but I'm sure the Bulls won't be looking our way. Not for that package at least. Maaaaybe Lauri + filler for DeRozan, either Murray/White, and a first would get it done, but I'd pass on that deal personally.