Your plants are not lavender. Looks like mexican bush sage to me...salvia leucantha.
They are drought tolerant and are also sun lovers.
If you are along the coast they should be fine in the winter, but in cold areas they do die back in winter and can be cut way back to near the ground.
The flowers don't last forever, they do die off so just simply deadhead them.

thanks! should i remove the dead stems entirely? do you think the stems that still have a bit of purple on the tips are ok or are they unsalvageable at this point?

definitely Mexican Sage! my favorite!

your plants actually look healthier than a couple in my yard (one was transplanted about 7 mo ago, the other newly planted about 5 mo ago).

mine is under a rosebush that seems to have a fungus, so i wonder if the fungus got to it?

anyway, good luck and enjoy the lovely scented sage!

They are in fine shape IMO. Just dead head the dead flowers, cut them back to the first set of leaves.
The quicker you dead head the more flowers you get.
Once each one of the flowers die off then cut them back.
Hummingbirds like them so when you aren't home they might be around...please don't take away their food source.
There is no need to take any drastic cuts on this plant.
They really are doing fine.
If the house was vacant for a while you might give them a very light fertilizer.
Once you cut all the dead flowers it will look 100% better.
They are tough and I think they tolerate a lot.
They survive here in my area in 90+ all summer but die back some in winter. So if you are inland in the heat they might suffer a bit in Sept-Oct.

thanks so much for the tips! i've actually been looking for ways to attract more birds to the yard, so it's pretty cool to see the note about the hummingbirds

Almost anything flowering will attract birds and bees.
If you want hummers, think salvias/sages especially S. greggii. They are hummer magnets.
Beware of fruits, berries etc cuz then you get even more nasty droppings.
Almost any deep throated flower will attract them. I have different things flowering all year for them to feed on.
Cape Honeysuckle not the honeysuckle vine will flower in winter to spring.
Also a nice little water fountain or bird bath they will all enjoy if you can keep it clean and keep the crows out.

Pick up the Sunset Western Garden Book available at any book store, online or Lowes, HD etc.

cool, thanks! good call on the droppings, i didn't even think of that... :) the cape honeysuckle looks beautiful... i'll definitely take a second look at that once i get the yard weeded + i can start having some fun introducing new things to the yard...

Ditto on the Sunset Western Garden Book... it's a lifesaver.

One other thought on the Mexican sage - it's nearly indestructible so if you want to cut it way down now or over the winter, do it. If you want to trim carefully stem by stem, that works too. I have a bunch in my yard and the hummingbirds love it.

Enjoy the new yard.

In late winter when you start to see new growth coming from the soil, cut the old growth completely right down to the ground. The plant will come back refreshed and gorgeous for the new growing season.