I assume you are talking about the plant that has the purple/fushcia flowers on it?
I'm not sure what it IS< but its NOT a lavender.
If you are talking about the grayish foliage smaller plant in the foreground of the other one, that appears some type of sedum.
sedum would do well in your area. lavender may do ok, I don't know much about it. Maybe rosemarry or thyme would do ok too, all are fragrant herbs. Sage may be what you are looking for. I would suggest visiting a nursery in your area. or joining a garden club!
