Yes the rod goes through the butterflies and rotates...this is the area to lube.

 

I've seen "cautions" NOT to use "carb" cleaner on a throttle body, because is will remove the coating put on the blades to help them shed carbon buildup. That's why they make "throttle body" cleaner. I honestly dont know whether the LT1 TB blades have these coatings.

What plate gaskets are you talking about. The bottom plate on the TB contains the IAC passages and the coolant (assuming its still connected). I leak of either air or coolant into the IAC passages will screw things up badly. The top plate covers the chamber that connects the valve cover air supply hose to a port that starts in front of the throttle blades. A leak at that point would pull dirty air into the intake. Why would you NOT expect to find gaskets?