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).

Carsten Shultz' answer is still generally correct, but there's also the easier option to use a tool like Diskmaker X http://diskmakerx.com/whats-this/ or since Mavericks use the built-in ability to make a bootable disk with a Terminal command.

For the latter with the Mavericks or Yosemite installer

1. Start the Mavericks/Yosemite installer that you previously downloaded and stop at the first screen with the big X symbol and continue button.

2. Open up Terminal and if Mavericks, then issue this command on a single line:sudo /Applications/Install\ OS\ X\ Mavericks.app/Contents/Resources/createinstallmedia --volume /Volumes/[DiskName] --applicationpath /Applications/Install\ OS\ X\ Mavericks.app --nointeraction

   replacing [DiskName] with the name of the disk you want to reformat into an installation disk. If there are spaces in the name use "quotation" marks around the whole path: "/Volumes/[DiskName]". Alternatively, if Yosemite issue this updated command instead:sudo /Applications/Install\ OS\ X\ Yosemite.app/Contents/Resources/createinstallmedia --volume /Volumes/[DiskName] --applicationpath /Applications/Install\ OS\ X\ Yosemite.app --nointeraction In both cases you of course need to supply your administrator password as usual.

3. Wait for the installation to complete, This can take a very long time, like an hour or so, depending on the speed of the disks involved and other factors.

With the OS X USB Installer disk ready follow Carstens's advice and hold down option after reboot and boot up from the installer and unfettered from the installed OS X on your internal disk install the OS X version on the external disk of your choice.