You are not allowed to download an additional copy of Lion on the new MBAs or Mac Minis because it's already installed. Saying that you can't install Lion is something totally different.
If you restore the ESD image to a USB thumbdrive you can boot any mac with 64 bit processor but not the MBA (haven't test with the mini though).
If you dig deeper, you can restore the BaseSystem image and it'll boot, but it'll say "this version of mac os x cannot be installed on this machine". Then if you hack the installation file a little bit it'll allow you install but you won't be able to boot.
Then if you have access to the 10.7.2 beta update, you can run it from the command line and voila, your MBA would finally boot.
I know these 'cuz I tried to fix my MBA for the last 2 days.