Lavender smells of clean linen, and most accounts say its name means "washing." The trouble is that the dictionaries do not agree.
The English word goes back to around 1300. Etymonline traces it through Anglo-French and Old French lavendre to Medieval Latin lavendula, recorded in the 10th century. That much is settled. The argument is about where lavendula came from.
The popular answer is Latin lavare, "to wash." Wikipedia's article on the plant gives this as the usual view. It ties the name to blue infusions of the plant used for bathing. The story fits neatly, since lavender scented bathwater and freshly washed fabric, and French lavande and Italian lavanda look like washing words.
Some dictionaries are not convinced. Dictionary.com treats lavendula as a variant of livendula, from an unrecorded lividula, "a plant livid in color." That points to Latin lividus, "bluish," the source of English livid. Etymonline offers lividus with a "perhaps." It allows that the name may instead have been linked to the washing words because of how the plant was used. On that view, washing is how people explained the name, not where it came from.
The bathhouse picture has a gap too. Wikipedia reports that researchers who looked at writing on bathing in the Roman Empire found no mention of lavender. The image of Romans perfuming their baths with it is poorly supported.
The color came much later. Etymonline dates "lavender" as an adjective for pale purple to 1840, and as a color noun to 1882.
One more twist. Middle English had a second, identical word, lavender, meaning a laundress or washerwoman. Etymonline finds it as a surname from the early 13th century. A laundry word that sounded exactly like the plant may well have helped the washing story stick.
Whichever origin is right, lavender now sits beside a large family of washing words. Latin lavare gave English lavatory and launder. Etymonline lists the same root as a possible source of lotion and deluge as well.