According to the manufacturer the game under Max OS X Lion is not supported. And after downloading here at Amazon can not start the game, in fact. Fortunately there is a solution: we have to replace the default installed "Ubisoft Game Launcher App" by another. An Internet search for "Solved: Conviction Launching Issues on OS X Lion" brings (the Ubisoft forum) quickly the solution.
The game itself runs extremely well with me: Mid 2011 iMac 2.8GHz Core i7, 12GB RAM, AMD 6770M 512MB. It can also play without an Internet connection.