Lavine makes no sense while having both DLo and Reeves. You cant get assets for DLo on an expiring, so it's kind of out of the question to get LaVine.
Ingram would be a good option, but why would NOLA want any of the players they could offer? The Lakers salary matches are complete meh at best, (Rui/Vincent/Vanderbilt at a combined 38 million).
Lavine would only be coming in if DLO is being sent out. I'm not actually sure if Lavine wins you more games during the RS due to his health issues....but in theory is a good fit with LeBron.
NOLA would consider it because Lakers can put good picks on the table. Ingram's cost doesn't seem very high atm.