How can Proxy and Facade design patterns be combined?

I have a third party library class Lib and an own LibProxy where LibProxy adds some caching before passign the control to Lib. This would have been textbook Proxy, but LibProxy also simplifies the interface to Lib. Which also makes it a Facade.

What is the course of action here? Making LibProxy comply to the interface of Lib and adding a separate LibFacade feels like overkill. This is what it would look like: Client->LibFacade->LibProxy->Lib.

Can I call it LibProxyFacade instead? Or is there some other pattern that is equivalent to the Proxy/Facade combination?