Heavy clay here. I would suggest planting the rosemary, thyme, lavender, and sage in a raised bed with exceptional drainage and soil that is not very rich.

Many medicinal herb plants native to the Northeastern US, have no problems with the heavy soil.

FataMorgana

In many cases, clay soils are just fine for almost anything you wish to grow. However, if the site is clayey AND does not drain decently, then there can be some issues. There are some other factors, too. What color is the soil? Color can tell quite a story.

My entire property is built on a very heavy clay soil which is red in color. It drains very well (for clay), and I have come to appreciate it very much. We amended the planting beds once when we originally designed and planted the landscape but never since. Anything that is planted in those beds or in the lawn (as in trees) receives no amendments whatsoever, which is the accepted horticultural practice, even for clay soils.

Everything has flourished, including a wide assortment of culinary herbs not generally recommended for clay soil.

Of course, it goes without saying that I never over water.

I have clay soil, which I've amended with a lot of aged horse manure. Hidcote lavender has done very well for me and I water it a lot, since it's in front of my roses. It made it through the winter with no problems, has a lovely fragrance and very pretty purple/blue flowers. It's also a great deer deterent :)