I have some old LMR Freight WTTs, but not the East Lancs lines, and not quite your vintage either.
The ones I do have contain "universal" letter and symbol codes appearing between the hours & minutes, which are listed on the front pages of the timetable.
These include things like:-
c - arrives 2 minutes earlier
L - stops to change locomotive or enginemen
PB - stops to pin down or pick up wagon brakes
Q - runs when required
t - stops only for tablet, staff or token purposes
* - stops or shunts for other trains ahead or to pass
But there is never a V in these lists
Within the body of the timetables, V does appear here and there - always with an explanation somewhere close by as to what it means.
On a quick scan of WTT I have, V seems to indicate that the time applies at a location close by, but not the same as the location tabulated in the left-hand column.
Almost as if "V" stands for "Variation" (no idea if this is the true origin)
Two examples:-
- Timetabled row is for Carlisle Yard - train time shown as 02V01 - note in same column says V - Carlisle Station
- Timetabled row is for Edge Hill Exhibition Jn - train time shown as 08V10 - note in same column says V - Picton Road Jn
Obviously I can't say whether same interpretation applies in your 1956 edition, but I'd suggest looking for an individual explanation of the "V" close by.