I'm under the impression that the built-in AirPlay Mirroring functionality is specific to Mountain Lion. Which is OS X 10.8.x (current version is 10.8.2)
While I think it's always a good idea to run the most up-to-date software, unless a 3rd party application has a known conflict, updating will not enable this function in Lion.
I've used AirParrot - http://airparrot.com
It's $9.99, so 1/3 the price of Mt. Lion.