Typically the spindle is offset on that type of pedal, so if you use it right side up your foot doesn't press hard on the center of the pedal, or the center area around the spindle is flattened for comfort. The other side often has the spindle area bulging up. If they made the pedal symmetrical you'd be more likely to catch it on the ground leaning into a turn.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72