1. The Lakers have to give him a contract extension
There is no way the Los Angeles Lakers are trading for Kyrie Irving without extending hs contract. Irving has a player option this offseason and that does give him some leverage in the situation. If the Nets do not want to extend him then he can opt out and there will absolutely be a team that is willing to give him a max deal.
If LaVine were to come to the Lakers there would have to be some pressure from LaVine and his camp (Klutch sports) to essentially force him to LA and not give any other team a chance to sign him. Irving probably is not going to play that same game and will instead take a contract from whichever team is giving him the max.
And while he definitely is polarizing, he is still an All-NBA guard that several teams would talk themselves into signing this offseason. There is no question of whether or not he would have a market for a max deal.
Thus, the Lakers would have to execute the sign-and-trade with the understanding that they will give him a new contract extension. There is some flexibility with Irving that the team does not have in trading for LaVine as well.
A potential LaVine deal would be a true sign-and-trade that would hard cap the Lakers at the tax apron. The team could still do the move but it would literally have to only sign minimum players to fill out the roster.
With Irving, he can opt into the last year of his deal, get traded and then sign an extension on top of that final year on his contract, allowing the Lakers to go over the tax apron.