I prefer an Aussie Locker over a LockRight; however, the design is essentially identical. I believe the Aussie is a better product because it is stronger (less people break them) and the springs are softer allowing it to unlock easier.
I run a Detroit rear and an Aussie front without problems. It will create some crazy handling situations on snow & ice, but as long as you're careful and drive slow it can be managed. Off road my Aussie seems to work as well as my Detroit in the rear. It locks completely when torque is applied and makes minimal noise.
You don't have to worry about driveshaft orientation (as long as they're straight). All mechanical lockers like the Detroit, LockRights, Aussie Locker, etc., lock when torque is applied and unlock when one tires rotates faster than it is being driven. This is why the inside tire chirps going around corners on pavement.