"Phil. I'm glad this one has come up. According to the book by Alex Moore the second step goes across the LOD starting diagnal to the wall. I don't think there is any argument there. I also have a tape by Richard Gleave who introduced that the second step is straight forward on the same line as the first step near enough. And he says drive it forward."
This is patently obvious - you commence to move DW, and continue doing so. It is only as you lower from the third step that the direction of movement becomes backing LOD.
Now the non-obvious part is that this concerns only the direction of movement. During the course of this, the body has rotated, even before the direction of movement changed. That is why we can describe step two as a side step - by the end of the step, the action has become sideways by virtue of the fact that the body rotion means that the original and still mainted direction of movement is now appropriately called sideways.
"I also have a tape by Steven Hillier who actually says that Alex Moore in his book was wrong and the step does not go across the LOD."
You obviously misunderstood, as it is quite obvous that the step will go across the LOD, given that the direction of movement is still to DW.
"You are backing diagnal to the centre. It is then necassary to turn on the spot to find the LOD."
It is not really necessary to orient to LOD until partway into the next step... "always have a side left to swing" sound familiar?
Note that this means that your thighs will strongly close as your body rotates as you move into that next step.
"This for me is where it falls down. If I am from an Overturned Spin Turn go into Turning Lock I am in one hell of a mess."
No, you will be fine. Keep your direction of movement clear. Let your body slowly swing through neutral, and onwards as you are presumably aiming for the side lead of promeande.
"For those who do the first example will take their fourth step down the LOD. For those who step across will take their fourth step diagnal to the wall."
What you really mean is that those who step SIDEWAYS across the LOD, instead of swinging forwards across it as they rotate, fail to control the movmentum of their natural turn. Due to this failure of control, they are unable to direct the next step in the proper new direction of movement (down LOD) and instead let it drift off to the wall. In plain English, they have dances a quarter turn from the quickstep rather than a natural turn from the waltz.