HA does indeed have a lounge at LAX for Premiere Club, status, and F passengers but with very little food and drink available like it's lounges described in the islands.

Since moving to HNL earlier this year I have split my flying between UA and HA but in your case I'd definitely go the UA route because you'll get miles for your transcon/TPAC flight which you wouldn't get with the HA flight. The only flights on HA that qualify for UA/*A codeshare miles are interisland flights in direct connection with a UA flight from the mainland, which would work in your case if make a direct connection in HNL.