Thin and impoverished, i would think neutral to alkaline too.

They must have full sun, too.

Do you mean in a pot? If so, ordinary multi purpose compost, or John Innes No. 1, will be fine.

Even although they dont mind poor soil with young plants or new plants I would give them a good start in some compost and also regular watering till they have clearly settled in well.

thankyou to ever one x

Lavendula stoechas prefers an ericaceous compost.

Um, sorry to disagree Volunteer, but that isn't quite accurate - L. stoechas are found in the wild in slightly acidic conditions, but are very happy to grow in alkaline soil - they merely tolerate a degree of acid rather than preferring it.