On the '01 through the '04 LB7, I really don't think it matters because of a constant 80+ psi of pressure in the cooler flow. You won't get any air pockets. In '04.5, Allison started using the G solenoid which dropped pressure 150psi at below 8% throttle to take the load off the pump and cool better at idle. There might be a possibility for some air to get in the cooler since the cooler line will hardly dribble at idle and go full line pressure at above 7% throttle. You will notice that from '06 on, the coolers fill and exit from the top. I'm assuming they want to make sure there is no air pocket inside. Either way I don't think it amounts to a hill of beans which way you mount it.