With MacOS X 10.7.5 you can run Aperture 3.4.5, see: http://support.apple.com/kb/DL1657
Only, you cannot buy it from the AppStore. Try to buy a boxed retail version from Amazon or similar.
This will install an early version of Aperture, Aperture 3.1.x or Aperture 3.0. You can update it from the Support page, using the link above to Aperture 3.4.5.
But it would be more economical to upgrade your Lion to Mavericks and to buy Aperture from the AppStore, if it is feasable for you.