As a power washing company in TN, would I have the valid right to file a lien when unpaid?
Generally speaking, there must be a permanent physical improvement at the project site for mechanics lien rights to arise. So, things like cleaning and maintenance, which must be done on a regular and recurring basis, typically won't give rise to lien rights. And, because pressure washing isn't something that permanently alters the property, it doesn't fall into the category of work traditionally thought of as "lienable."
That said, TN does appear to have relatively relaxed definitions for what's considered an "improvement." This includes the "cleanup" or "removal" of waste from real property. So, the argument that pressure washing might be lienable is probably stronger than Tennessee than it is in most other states. Still, I'd be hesitant to declare pressure washing as lienable work.