Unable to install Xcode on a freshly-installed OS X Lion
I have a similar setup, but I've got 10.6 on one partition, 10.7 on another and 10.8 on yet another partition.  When the Mac App Store looks for installs, it will look at all the partitions for installed apps.  I think that is your problem: it is already finding Xcode on your 10.6 partition.

Here is how I solved it and how I recommend you to do it as well:

Unmount your 10.6 partition after you boot into your 10.7 partition


If you want to do this automatically, you have to edit the file:

/etc/fstab


Inside of /etc/fstab, you need to place your partition's UDID like so:

UUID=68613ECB-3492-3B8B-9FFF-55FB1F30A32B       none    hfs     ro,noauto


noauto means don't automount it.

To find the UUID of your drive, launch Disk Utility, select the partition and then press the Info toolbar button.  It will show you the UUID listed as Universal Unique Identifier.

Then reboot and you should find that your 10.6 partition is automatically not mounted.

At this point, the Mac App Store should look for Xcode, not be able to find it, and then allow you to install Xcode properly.