Yes, it's a harmonious interaction among plants, it's just that the technical approach on Holzer's diagram is based on taxonomic classifications., and that identifies the categories from which to choose the companion plants. Using your example of lavender as a deterrent, it helps to know that all lavenders belong to the genus Lavandula of the family Labiatae that include the thymes, basils, sages and rosemary. So it follows that if lavender doesn't grow well under some conditions, we can pull another related plant that will help in the same way. It's not just from observing, there are inherited, chemical traits that are present.
But not all plants want to be next to a plant with aromatic oils. My tomatoes hate lemon balm. Lemon balm is a member of the Lamiaceae (mint) family, (Melissa officinalis) and so it would follow that tomatoes don't want to be near anything in the Lamiaceae family, so keep away catnip and spearmint as well. And it also follows that all solanums (not just tomatoes) don't want to be near something from the mint family, and that includes peppers and potatoes . So it's less of a hit and miss association.
It also helps to understand the mechanism by which the plants are doing what they do. Mints provide something very different chemically than the Labiatae family. And knowing why plants are companions or not is also very helpful
"Life flows on within you and without you"...George Harrison
Coastal California, USA, Mediterranean climate - no summer rain, a little frost mid-winter