CJ you're absolutely correct, the Lightning had a very good autopilot (Smiths MK 10 I seem to recall), You could use it either in Ht & Hdg mode or in Attitude Hold. In either mode you could select the autopilot and then fly the a/c on the 'little stick'
The incident you refer to did indeed happen. An Air Commodore (I think) wanted to fly the a/c solo and duly underwent a short course. Your first solo was at that time flown in the T4 so off our hero went. On finals to land, he decided to use the autothrottle to keep the speed @175kts but forgot to disengage on landing. He kept pulling the throttles back, not an easy task against the clutch, as soon as he released any pressure on the throttles they moved forward again trying to keep 175kts, the autothrottle won and the barrier saved the day.
The auto ILS was super, so accurate that the decision ht for an auto approach was lower than a manual ILS. There used to be a bit of discussion at Wattisham about the possibility of doing an auto ILS at Honington if you were really caught out by the Wx and lack of fuel and just letting the a/c hit the ground, Honington having an in-line ILS al the time, would have been quite exciting but some folk were quite certain they would give it a go.