Even though Lebron has not said it publicly that he would bring the Lakers to the Finals this upcoming season but that is what the people expected of him. When he was with the Heat and Cavs the teams always appeared on the Finals with Lebron on it. Maybe that is the reason why Lebron's team mate at the Lakers right now are pressured to play well so that the Lakers will be in the final as to not tarnished or end Lebron's consecutive run to the finals.
I don't see it that way. Most people now are not expecting Lakers to be in finals and we all know that the chances are now became slim compare when he was on the East. Not just with Houston Rockets and Golden State Warriors but West competition is really tough.
His transfer to Los Angeles Lakers is different from the status when he transferred to Heat and returned to Cavaliers. He joined Lakers without any superstar on it and coming from a worst record so I don't think it's only about a championship goal but yeah an expensive max contract.
I will give 50/50 "for now" for the Lakers that they will reached the finals and 80/20 that they will reached Conference finals.