The Lutzow v Spearfish radar usage is interesting. Can you give me your source for
Luetzow had detected the surfaced submarine with Seetakt radar, at a reported 15,000 meters. Unfortunutely for the Germans, Thiele closed range to investigate the radar contact. When the radar contact dissapeared it was obvious that it was probably a submarine that had sinced dived.
Cajus Bekker "Hitler's Naval War" describes the incident the same way, radar contact 6 degrees to starboard 15,000m but Koop and Schmolke apparently quoting the KTB put a completely different slant. "01:20 Radar reports object astern
at 6 degrees, 1.5km. 01:26 Turned to port at 1.15km. Nothing seen, no further radar contacts, starboard rudder to original bearing to get us through Skagen Narrows as soon as possible. 01:29 Ship still turning. Enormous shock astern. Torpedo track reported acute angle port side. Assume submarine attack."
Ewart Brookes "Prologue to a War" devotes a page to describing Lutzow's routing further offshore to avoid known British submarine operations, and Spearfish on the surface recharging exhausted batteries after a 60 depth charge pounding, spotting a wake in the dark on her beam. Initially Forbes in command thought it was a destroyer and turned away, but then he realised it was a large ship turning away itself, so swung round again for an attack on the surface. When Lutzow back toward him he fired six torpedoes, hitting with one which blew off both props, collapsed the stern and crippled the Panzerschiff. Spearfish was still damaged from the earlier depth charging so Forbes slipped away, still on the surface in case there were escorts.
I have to say that the idea of an unescorted Panzerschiffe deliberately sailing up to contact in the dark from 15,000m away, when British submarines had attacked a nearby convoy sinking a couple of transports and an escort, seems most unlikely. Much more likely seems the rangefinder mounted Seetakt missed Spearfish altogether until Lutzow had passed her before getting contact at almost point blank range true bearing 006 degrees. Lutzow's high speed and course changes meant only one of six hit, and either these were Spearfish's last torpedoes or withdrawal meant the crippled ship survived to fight another day.
The Luetzow had been making flank speed at the time the radar detection of Spearfish was made, so it's unlikely that passive or active sonar would have been in use.
PG's GHG was in use at 28 knots in Denmark Straits whereas Lutzow was only doing 24 kts. Still no evidence of GHG installation or use in Lutzow.
All the best