I'd like to buy a new Air (I'm currently using the 2010 model) but I'd also like to avoid having to use Mountain Lion (It has worsened the performance of every machine I installed it on, and adds nothing I'm that interested in).
Is it possible to erase the SSD and install an older OS than shipped on it?
Mountain Lion will only worsen the performance of machines that are stuck with 2GB of RAM. Period. Even if you are rocking any Mac with 4GB of RAM, including the oldest generation of MacBook Pros that can run it, you will actually find that Mountain Lion is FASTER. That is...unless you have pre-existing software or hardware problems that have nothing to do with the installation of the OS itself.
That being said, you can wipe your machine and install Lion if you so desire. The current MacBook Airs originally shipped with a system-specific build of 10.7.4 before Mountain Lion came out (and then were thusly shipping with Mountain Lion) so as long as you can find and install either that specific build of 10.7.4 or a generic 10.7.5 Mac App Store version, you should be fine. Though again, I don't know why you'd want to. Any current MacBook Air will run Mountain Lion so much nicer than Lion.
The earliest version of OSX you can install is the version it comes with. Since Lion does not contain the drivers for the Ivy Bridge chipset you'll not be able to load it
Uh...Lion (with system specific builds of 10.7.4 and the retail version of 10.7.5) definitely contains drivers for all Mid 2012 MacBook Airs and MacBook Pros (including the 15" retina) and their Ivy Bridge chipsets. What it doesn't have is drivers for any 13" retina, any Late 2012 iMac or any Late 2012 Mac mini. Nor does it have drivers for any of the Early 2013 retinas. But the mid-2012 machines originally shipped with Lion, and the logic board part number has not changed since release. The only thing that has changed is that they now ship with a retail build of Mountain Lion preloaded and will allow you to use Internet Recovery with Mountain Lion rather than with Lion. Other than that, there's no difference.
Therefore, if the OP really wants Lion on that machine, then all he/she needs is a retail installer for 10.7.5 and they'll be golden.