Don't know, you will probably get a variety of opinions on that. Some people feel the operating system originally shipping on a Mac model performs best, since Apple would have optimized it for their current products.
Probably has a lot to do with what software you plan to run. Newer software may have problems on older operating systems. Frequently I see software saying that you need at least 10.10, however I found they usually still run under 10.8.5. I think companies just CYA and don't want to support a product on an operating system that Apple no longer supports.
When I got my MBA in 2011 I was just amazed by how fast it was, it ran circles around my 2008 15" MBP. If you are happy running 2011 era software, then I think Lion would be fine. Where you'll have trouble however is with applications like recent versions Safari and Chrome that won't run on old operating systems, and that raises some security concerns. There may be another browser that works however, not sure.
Apple stopped updating Lion and Mountain Lion, so any bugs or security holes will not be fixed (not sure about Mavericks?). The Mountain Lion update added a number of new features IIRC. I don't think 10.7 has an app store for example, and I don't think it support the Messages app either. I remember these being two nice upgrades when I got the 2013 MBA with Mountain Lion pre-installed.