LA's MTA has a bike locker rental program, find out here [1]. It's worked for me; stash a beater bike at the "work end" of the train commute and ride the "last mile".

If the "work end" is in Burbank, here's the info on their bike locker rental program [2].

There may be a wait list.

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[1] http://www.metro.net/riding_metro/bikes/images/locker_rental...

[2] http://www.burbankca.org/transportation/resources_lockers/lo...