Hi Gloria. If it has a fruit it's probably not Lavender Lady but an Amethyst. They pretty much look the same but the LL is a sterile variety. They would probably love your climate. Just plant them along your fence.
Karyn

Thanks, Karyn. That's where they will be going. So glad to hear they like it hot and dry. Looking forward to attracting the bees and the butterflies (and catapillars, too!) Hope to see some bats, but they don't seem to come up this high in the foothills. My son has them (he supplies houses for them) down in the "flatland"!!) Sure appreciate the good news. Gloria