From an LA Weekly story from January of this year:
"Robin Smith at Mud Creek Ranch (Santa Paula) sells the fruit as Persian sweet limes at the Ojai, Hollywood, Santa Monica (Wednesday) and Santa Barbara farmers markets. Jeanne Davis (Fallbrook) sells a slightly larger variety at her stands at the Beverly Hills and Hollywood farmers markets. Both have said they'll have the sweet limes/lemons well into spring."
That last bit, about having them will into Spring, makes me suspicious that you may be too late for them.