Can I run the game Civilization on mid-2011 MacBook Air? Is there any version of the game Civilization that will run reasonably well on a mid-2011 13" MacBook Air (1.7 gHz core i5; 4GB RAM) that shipped with Lion but now runs Mountain Lion?

PowerPC software won't run on Lion or Mountain Lion, and the graphics performance might preclude the latest releases, but is there any version modern enough to work with Lion/Mountain Lion but old enough that the graphics on an MBA will handle it?
I have the same generation MBA.  You don't specify 11 or 13 inch, and that makes a potential considerable CPU difference, but on my 11" 1.6Ghz 4Gb RAM Air I have played Civilization V just fine.  Slows down a little as the game progresses, but looks good and plays perfectly acceptably to me.