I have published several such models. I doubt the lid driven cavity is a particularly useful geometry for real world applications. These are most often used to visualize and test computational models and methods of solving various partial differential equations.
As I explained, I don't know that there are any real life application of the lid driven cavity problem. Most real life applications have much more complex geometry and boundary conditions.
It's like flow over a flat plate... used to illustrate many developments and derivations, including boundary layers, beginning with Prandtl. The nearest thing in the real world to a flat plate is perhaps an airfoil or propeller blade.
In the lid driven cavity (with origially stagnant fluid) a slip-wall would not induce any flow within the cavity, while die to viscous entrainment a flow is induced for by the lid wall.
For a slip wall any velocity tangential to the wall is allowed at the slip wall. This velocity is derermined by the flow in the cavity. In a lid flow cavity the fluid velocity at wall is equal to the wall velocity (in a continuum approximation for a viscous fluid).