No. The lips themselves are a vibrating system. I don't use the standing wave terminology but there are pressure reflections from the air column in the horn that assist that system and help stabilize at a pitch, but the lips are not starting and stopping a buzz.
The lips move open and closed during the buzz. But that isn't necessary either. You can blow a steady stream of air at an object, like the edge in a flute tone hole, or a high voltage wire, and get an oscillation.
