Which two keys are you referring to? For me neither of the 8x8 grid buttons work after stopping/starting my application.

Yeah, the same for me. I was referring to these keys in the context of Fons' solution which could be implemented in a driver.

The problem is basically that the LP doesn't send full midi messages but only the type (CC or NoteOn/Off) for the first message and then just messages without the type specified for any subsequent message. If you switch application in between then the program won't know what type of message you are talking about anymore. You can test this out by pressing on of the buttons that sends a CC (top row) and then immediately restarting your application. Now the top row won't work until you hit one of the grid buttons.

As for a more immediate solution. Have you tried sending the LP two remap messages (i.e. CC 0 2, CC 0 1) before quitting?