No offense to anyone and I certainly do not keep up on tire technology but in my 15 years as a master technician, secondary, and post secondary instructor, I've never heard this...
Crossing keeps the tread from feathering on the leading edge. A simple internet search will show multiple patterns for RWD and 4x4 vehicles ALL indicating a cross pattern. If someone knows something, I'd post it instead of offering advice based on nothing or habit.
Still trying to figure out the locker thing. I think you have a tire that is low and causing a pull...not the locker.