Like Jon, I have always used SD to clone my main boot volume while that was running. Never a problem. That said, (and with the occasional exception of a safe boot) I follow the manual's recommendations.
While stating that this is not strictly necessary, the SuperDuper! manual recommends in Step 1: Prepare for your backup to quit all running applications, and perhaps even do a safe boot into the volume to be cloned. Final note: I am NOT running Lion, but Leopard (PPC Mac).
