I have a thriving olive tree in my garden and I underplanted it with lavender, but that is not thriving. What other Mediterranean flowering plant could cope there? It’s in a south-/south-west-facing border, with clay soil.
Having its feet in heavy clay will make lavender sulk, however much sun it is getting. That goes for many Mediterranean species. You may need to dig grit around the olive before you plant anything else. The olive has deep enough roots and won’t mind bedding down in clay, but small perennials will. When I say add grit, I mean about 50%, and fork it in rather than dig it.
Eryngium and echinops (‘Veitch’s Blue’ is the smallest) may be on the tall side if your tree is small, but they will cope with your conditions: they are said to need sandy soils, but survive well on my clay and are tough enough to take the competition of the olive. For something lower, oregano should be happy there, as would rosemary and sage. You don’t have to stick with ordinary marjoram (Origanum vulgare): O. ‘Herrenhausen’ is slightly taller, with striking purple flowers, and O. ‘Rosenkuppel’ is compact, with larger than average flowers.
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