Although the electronic lockers are no longer available, most airports still do have some kind of baggage storage available. I believe LAX has a Baggage Storage Service that you could use for the day.
Check the LAX web page (under Passenger Services):
http://www.lawa.org/lax/laxframe.html
"This service is located on the Lower/Arrival Level of Tom Bradley International Terminal.
Storage hours are from 9 a.m. to 9 p.m. daily and wrapping services are available from 8 a.m. to 11 p.m. daily (Pacific)."
LAX International Baggage Service
380 World Way
Los Angeles
CA 90045
(310) 646-0222
(310) 646-0223
I think your EVA Air flight departs from this terminal, also, so that seems fairly convenient. You could give them a call to confirm storage details.
[This message has been edited by Abby (edited 08-04-2003).]