real talk:
lloyd's concept design looks like he was originally left handed.
he's right handed in the finished product though, obviously.
i assume he was made right handed ingame to fit the camera angle in battles better so he would have his front to the camera in a battle stance.
or maybe the right handedness came even sooner than that.

i also think that's why his exsphere is on his left hand — because he was originally meant to be left handed.