Lavender Not Growing Well in California

I have two pots of lavender and one of them is not looking very good at all. The leaves are shrivelled and looking dry and the flower bud heads are dropping down. Have I over / under watered it or is it not getting enough sun? (I live in Los Angeles.)

I assume your two lavender pots are not in the same sort spot in regards to exposure to light? If the plant had too little light it would be stretched out (etiolated) with thin long leaves and long distances between successive sets of leaves. But since you mention flowers, I sort of doubt that. It would not bloom if it is kept too dark.
Lavenders must have excellent drainage. Is the pot in question supplied with holes in the bottom that allow the excess water to drain out freely? In the winter lavender should be kept drier and over-watering will make it rot rapidly. Check if you see any rot- that is mushy smelly stems and leaves.
If you have kept the plant so dry, that the root ball dried out completely, then you will have caused a lot of the roots to turn to hay – i.e., die. The plant may not recover from that. If you suspect this, cut off one third of the top of the plant, water well and keep in a shady spot until new growth is well on its way, then move gradually back into full sun.