On an open-sighted medium to large bore double rifle regulation may be not influenced by r-l(u-o) or l-r (o-u) firing sequence, but on a dr regulated for scope use it certainly is. Reason: When the first shot is fired, the barrel heats up and expands slightly. This will bend the barrels in the direction of the still cold second barrel.On an open-sighted dr this movement is compensated for by the front sight moving in the same direction. A scope will not move with the muzzles. It is a well-known fact in Germany that a scoped double rifle must be regulated by firing the barrels not only in the same sequence every time, but for best grouping they must be shot within the same timing the regulator used. And, between "l-r pairs" you must allow for a complete cooling down of a dr.
Set triggers to both barrels were quite common on German-Austrian dr's pre-WW1. But be warned: never,never set both triggers! Doing so will make the rifle double all the time.