Two copies of Lion installed on one computer, now the App Store won't install apps
That the App Store application finds the apps installed on your other OS volume is a feature. It may not be exactly what you want in this scenario, but consider the far more common scenario of a user moving some of their apps to an external volume because their system volume is running low on space.

You could file a bug with Apple, but the team responsible is unlikely to be convinced add special support for such an uncommon use case.

I'm afraid you're likely stuck with unmounting the second volume.