Just to add some clarification, if your MBAir shipped with Lion, then that is pretty much the minimum OS it will boot. And sometimes Apple will load a slightly modified version on there to support specific hardware in a new model. So even though the version might read 10.7, and you just installed 10.7 from the App Store, it may not work. The general rule of thumb is you want to be at least one point release above what shipped with a unit for a more universal bootable external. So if the mid-2010 MBPs shipped with 10.6.3, you want to have at least 10.6.4 on your external drive.
A lot of times, if you try and boot 10.5 on a system that came with 10.6 -- the same applies going forward -- it simply won't boot. You'll either get the Apple logo, but no spinning gear, or it will kernel panic fairly early in the boot process. The latter seems to be what's happening to you.
My mid-2008 MacBook Pro 15 died recently (motherboard failure)..

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