Well, due to the Coriolis spin imparted by the earth it depends on what hemisphere you are in. Check and see which way your toilet swirls to get an idea as to which way you should mount the burner. Don't want to be fighting the earths rotation, it'll decrease efficiency...

Makes absolutely no difference what side the burner is on, it'll work both ways. I think it's a case of monkey see monkey do on most. It is on the right side on my small furnace and the left on my big one.
The only problem you may find on that lawnboy housing is that you may have a shrinkage issue. Most aluminum alloys are going to show some shrinkage, and the copy may wind up about 1 to 2% smaller than the original. I suppose you could put several coats of thick paint on it to beef it up, and you can get a percent or two maybe when you rap the pattern to pull it from the sand. The dimensions may be a bit off, but you were probably going to machine the bearing surfaces anyways. That looks like it was originally die cast.