That doesn’t seem right, or I’m missing something. If I dam a stream and create a 12’ diameter pool, but the incoming water flows over the spillway, that’s a lake?
Of course, to confuse matters, a lake becomes a pond if damming was done by beavers.
Note that by the proposed definition, all rivers and all segments of any river are lakes; outflow is always equal to inflow for any persistent body of water.
Personally, I'd be more comfortable choosing whether to call Lake Travis a "river" or a "lake" based on whether there's a current on the surface. If yes, it's a river. If not, why not call it a lake.