Install an older OS X version on an external volume
The (or at least a) solution is embarrassingly simple: Do not start the installer from a running system, but make a bootable install medium from the disk image included in the install program package and use that.

Quick instructions (more detailed ones can easily be found on the net, but I have not read any thoroughly enough to be able to endorse them):


Take for example USB drive or SD card, partition it in Disk Utility, make one partition and make sure to select GUID partition scheme so that the medium will be bootable.
In Disk Utility use "Restore" to copy the Installer to the boot medium: As destination use the newly created partition, for the source use the Finder to show the package contents (right click) of "Install Mac OS X Lion", there locate InstallESD.dmg and drag it to the source field.
After copying, reboot holding the option key, select the install medium you just created and happily install Lion to a destination of your choice.


An 8GB medium will be fine for the installer (it's 4.7GB), and a 32GB partition for the installed system (this will leave you with more than 7GB of free space).