It seems like it should be fine in very small amounts, and make sure the dog can't accidentally ingest any of it.

So a bouquet of lavender stems on the shelf shouldn't be a problem, but lavender oil is so much more concentrated than a flower on a stem, so definitely don't use directly on the dog and don't use an oil diffuser in a small room with the dog present at all.

The article you linked is trying to promote its own brand of cleaners, so it may be a little confusing, but I think it boils down to "use sparingly and safely, and if in doubt don't use it at all"

ASPCA lists lavender as toxic to dogs

Dogster gives slightly more nuanced information showing it's toxic if ingested in high amounts.

VetExplains gives detailed information and suggests talking to your vet if in doubt.