Thanks Mike, I was waiting for you to jump in with the correct historical data.
Actually, the more I think about it, Lt. General is probably more accurate than using Lieutenant for the lower class of officer (2nd, 1st, etc.). The word lieutenant means a subordinate to a higher ranking officer. So a Lt. Gen is subordinate to only one class of General (two if you also count 5 stars, but that is a special case). IOW, we shouldn't necessarily use the order of the lower ranking officers as a guide to the general officer classes.
The general officer order is very similar to the Major, Lieutenant Colonel, Colonel order.