There are no lockers or luggage storage places at LAX

Honestly a rental car may be the best best for both storage of your clubs as well as getting around. Hollywood is far from LAX and not too easy to get via public transport.

If against renting a car, I would suggest the following: take the LAX FlyAway (motorcoach) to LA Union Station. They have a bag check service with requirements of anytime day of travel but 3+ hour minimum to check your bags. Its a $5 fee in addition to the FlyAway bus fee, so once you get to Union Station immediately check your bags for the LAX-MIA flight. Then, from Union Station you can explore downtown LA, or take the Red Line to Hollywood & Highland and see Jimmy Kimmel or at least his theater, Hwd Blvd, the Hollywood & Highland Mall/Kodak theatre, the Mann Chinese, etc. There is enough to do around there to keep you busy before doing the reverse back to LAX.

P.s. there is an email address for the luggage service at the FlyAway link I provided above.

Good luck & great find on the crazy routing to MIA!

p.s. - the NW WC should be open for the DTW red eye, you'll just have to deal with the China Air pax who also use the lounge and ignore the no-smoking rules.