Check out this thread, which specifically mentions Delta (and Hawaiian): http://www.fodors.com/community/air-travel/no-through-checking-baggage-after-jan-1.cfm

Then check out Delta.com: "Policy Clarification: Effective for travel on or after January 15, 2013, Delta Air Lines policy will be to check a passenger's baggage between the origin and destination points that are issued on a single ticket or conjuncted ticket exclusively. If a second ticket is presented for travel on another airline beyond the destination of the first ticket, the passenger will be advised that Delta will only check the bag to the destination on the Delta ticket(s). The passenger must collect the baggage at baggage claim for their Delta ticketed destination, and then re-check their baggage with the down-line carrier for the next flight(s)."

Then contact Delta. Don't hang up until you have a definitive answer.

Then consider traveling carry-on only if you want to avoid re-checking your bag with Hawaiian at LAX.

Yes, you will almost certainly have to reclaim your bags and check in again, so I'd allow a minimum of 4 hours, 5 to be safe. Most airlines will no longer check bags through unless you are flying on a single ticket. Hawaiian is not part of Skyteam, so I see absolutely no reason why Delta would check your bags through.