Of course the LEM wasn't tested on Earth--it was built for 1/6th G, it couldn't work on Earth. It's the same thing with the arm on the Shuttle--it couldn't be tested on Earth because it's built only for zero-G. It can't hold it's own weight in a 1G field.
As for the rover--it wasn't on the side. As you say, lopsided doesn't fly. It was put underneath--remember, the space outside the pressure hull is nothing like solid. The LEM was built for vacuum only, there was no need for anything resembling streamlining. Just drag it out when you need to. 435 pounds on the moon is within what they could handle by muscle power alone.
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