Cliff, it is very possible that the previous owner was also a lefty shooter and used the left barrel as his first shot. It takes some getting used to shoot the rear trigger and then move your finger forward for the right barrel as you have found out.
I am a right handed shooter and have a hammer gun that shoots the left barrel first. It doesn't look much different in this configuration when apart. You could probably do this yourself if you have ever taken an L.C. Smith apart, if you have not I would not recommend doing so as putting it together is tricky.

Using a gun with a selective trigger and trying to change the selector on an L.C. Smith is not an easy task would be more of a distraction trying to so this on a bird gaining distance between you and it.