I have a 20gb file that I need to back up and I don't have an external drive or access to any high-capacity cloud storage but I need to format/reinstall OSX Lion on my MacBook Air. On Windows and Linux it's possible to make a partition and just ignore it when formatting/reinstalling but being as ML will get pulled down through the App Store I don't want to risk losing the file. So, my question is: How (if at all) can I make a partition that the OSX installation program won't delete when I format and reinstall OSX?
Make second partition on the drive using Disk Utility and as long as you don't install to that partition, it will not get erased by an OS (re)install.
You should be able to live shrink your existing partition and create this new space at the end if the partition view of the disk.