Originally Posted by Aeroplane

If you want to go backwards. The only way to manage LSD for a single-speed would be to get a BMX hub that has reverse threading for a left-side freewheel. And adapting that BMX hub to work on your road/mountain/whatever bike would probably require a bit of hub surgery.

Going left-side drive with a fixed gear, on the other hand, is way easier. Just flip the wheel and throw the chain on.