The words matter. Here they are, cut & paste right from the COC. It's a travel certificate and it's not just if OP lives around LA, but if he originated at LAX. There is also a lengthy list of other exceptions which boil down to "if it was mechanical, UA will pay." Crew time out will depend on why the crew timed out. Not uncommon on TPAC because there is just so much tolerance built into the flight.
Lodging - UA will provide at its option either one night’s lodging, or, if no lodging is provided and upon the passenger’s request only, reimbursement for one night’s lodging in the form of an electronic travel certificate that may be applied to future travel on UA up to a maximum amount determined by UA when a UA flight on which a Passenger is being transported incurs Irregular Operations and the Passenger incurs a delay that is expected to exceed four hours between the hours of 10:00 p.m. to 6:00 a.m. local time. Where lodging has been offered but not accepted by a Passenger for whatever reason, UA is not liable to reimburse the Passenger for expenses relating to alternative lodging secured independently by the Passenger.