I grow lavender in clay soils without any improvement. But in locations which are kept pretty dry. At my previous house the soil was alkaline clay with flints. But the lavender was grown in very dry location, alongside a concrete drive, and raised up above next door's lawn.

At my present house, where I have a low lavender hedge along the front of the main laurel hedge, the soil is far from ideal for them, but they grow fine, have to be kept under control with hedge clippers. Most of my garden has a foot or so of light sandy loam above the clay-with-flints subsoil, but where the hedge is, the layer of loam is practically absent. But, again, it is a pretty dryish location. It is somewhat raised up above the lawn behind the hedge, and has a tarmac footway alongside it.

I don't know why lavender plants are so expensive in garden centres, I found them easy to raise from a packet of seeds. I suppose it is generally second year plants that they sell, so they have had to pot them on and keep them over the winter. Does that make them cost a fiver?