Lacing was used in aircraft since they started putting wires in them. Saves the weight of a full braid and allows for immediate repairs.
That manual is from the 60's and by then braiding was long gone away with due to the widespread use of plastic coated wires.... that and the Army would never be able to train skilled enough workers to deal with braided harasses.
This is a braiding machine in action:
Looks like a 32 spool unit. Early ones are just like this, but may be hand or pulley driven.