Newbie with no cluebie!

Can you also clarify the point about potted plants @DavidMey ? We weren't clear on whether you just meant buying plants in pots or growing them completely in pots.
Your location and general climate also helps with advice. No point in suggesting things that simply won't survive or thrive in your area.
The soil under membrane/gravel won't be plant friendly so there's no point adding anything until you open that up and look at it - especially for something like lavender, for the reasons given above re soil and aspect. The size of the plants [ie maturity] is a factor too. A tiny plant put in unfavourable ground at this time of year isn't likely to do well, compared with one that is larger, and is going in a good site

 

From the description of the "low maintenance garden" I am imagining it's all gravel/paving/artificial grass with no exposed soil to plant anything.

 

Lavender likes a sunny spot with well drained soil. I have clay so I dug in compost before planting. I'm in SW France so there is plenty of sun!

They will need cutting back to a neat shape after flowering (or in spring if you live in a cold area) but as @AnniD said, don't cut back into old wood.