You want to process the sound coming from another windows application in LiveProfessor and then output it.
There is no built in support for this in LiveProfessor, and it was not designed to do this.
That said, it is possible using some third-party tools.
You need two things:
Virtual Audio Cable (Or something similar)
This is an application that adds some virtual sound devices to windows and lets you route audio between them.
You can set Application A to use VAC#1 and set VAC#1 as the input in LiveProfessor.
If you are on OSX, there are other options like Soundflower or Jack
On windows you will probably need to set LiveProfessor to Windows Audio (not ASIO) under Audio & Midi options
For installation and setup you'll need to refer to the respective products.