There is a misconception of this floating around. What "fly" does, is that GCI sends flight direction to the plane and not that GCI actually flies the plane.
Lazur and newer systems inform pilot how to fly the plane for the ideal intercept and this data is automatically extracted from GCI radar plots, computed and then sent via datalink.
Pilot receives what speed, altitude, heading should he fly, and it also receives where to point his radar.... reading the manuals of these automatic intercept systems, it is amazing what level of automation was achieved already in the 60s.