Install Lion as second boot option on Mountain Lion machine
Use Startup Disk, in System Preferences, to change your boot disk. From there select the second partition. Restart with the Lion setup on a USB drive. You can install it from there.

If the above doesn't work try holding down the option key while rebooting. That should bring up recovery mode. From there you should be able to select the target volume for the installation.

Do a quick google search on making a bootable disk image either on a USB drive or on a dual-layer DVD disk with Lion by using Disk Utility. This is the method I used to downgrade a Mac from Mountain Lion to Snow Leopard. 

Let us know if you have tried the above options and what was the outcome.

Some useful links:


OS X Mountain Lion: Change your startup disk
Startup Manager:
How to select a startup volume
Make a Bootable Mac OS X 10.7
Lion Installer from a USB Flash Drive