"Alex Moore's book doesn't cover a V. Six. It does cover a Lockstep on pages 67 - 67."
It seems you have the 9th edition. (Why didn't I know that already?!?!)
The V-6 appears in the 10th edition where Alex says "The V-six consists of a Back Lock commenced with lady in line moving diagonally centre, steps 2 and 3 of the Outside Change (See Waltz section), and a Forward Lock diagonally to wall."
In the step description, step 4 (after the LF crosses) is given as "RF back, R side still leading" He does not comment upon why this differs from a normal back lock (RF diag back), which was the basis of the original question, irrespective of which side of the room it is danced,