Look up the different types of lavendars. I think this is a species that would not survive in zones 5, 6 or 7, but could be maintained in a greenhouse.

Lavender stoechas ssp. pedunculata - Spanish lavender. Not hardy here, but gorgeous anyway.

Actually Lavendula stoechas is hardy in zone 7. I grew it here over 3 tough winters before ripping it out of a spot with not enough sun.

I thought I had a lost a post! But turns out I answered this one in Perennials forum. Now what's a Mass gardener doing in Mid-Atlantic? :-) It would not be hardy in zone 5, that's for sure!

It does okay for me too in zone 7, although it looks a little ragged after going through winter. Perks back up though. Mine is in a sheltered, sunny spot that helps it survive the winter temperatures.

Here is a link that might be useful: recent post on Spanish L./Stickadove