If my understanding is correct, the Lakers weren't allowed to pay Caruso that much due to cap rules, not because they chose not to bring him back.
Looking into it, there were 3 different podcasts where the reporters said it was a tax issue.
Ramona Shelburne on the Hoop Collective pod: “Caruso was willing to go back for 3 years 30 million dollars. He gave them that option… the Lakers were willing to go 7 million a year.”
Sam Amick's on the Athletic pod: "There was a sense of disappointment on Alex Caruso's side there wasn't a Lakers push to keep him, like come in at 80% of the Chicago number. It was essentially a 'good luck in Chicago' type of feel to it."
"Amick hypothesizes that the luxury tax was the reason the Lakers weren't willing to match. He mentions how Caruso got the Chicago deal, showed it to the Lakers, and the Lakers didn't even counter. That must be crushing if you're Caruso, it's a tough business. "
and Lowe:
“Well look, the Caruso decision was a tax decision. Even the Russ trade, the tax was not
not a consideration. Because Schröder, plus Hield, plus KCP, plus other role players was probably going to end up being more expensive than Russ, even though Russ makes a massive amount of money.
“And look, you can sit here and quibble and say ‘how can you worry about the tax when you have LeBron James approaching 37, like you should be all-in to win now?’ But they worried about it, and that’s their prerogative.”
I don't see a thing about cap rules (but I might not be looking hard enough).
Edit: Silver Screen and Roll says "The luxury tax was certainly a driving factor in the Lakers’ decision, as no rules prohibited them from matching or even exceeding Caruso’s deal with the Bulls, let alone paying him an even lower salary. "