This wasn't the era of total situational awareness with GPS, satnav and instant communication. German Naval Command had no idea where the U-20 was, the British Admiralty only had an approximate idea where the Lusitania was. Heck even the Captain of the Lusitania wasn't exactly sure where he was, having misidentified Brow Head on the Irish coast earlier.
And the reason the Lusitania was sailing straight at constant speed was to take a four point bearing off the Head of Kinsale. It was a choice: take the bearing, or zig-zag to make yourself a harder target for a U-boat that might not exist, and be out of position and possibly run onto a rock that you know does exist (you're just not sure where you are relative to it).
Well, that's silly. In the first place, the U-boat in question (I forget the number) was out of his normal lanes and down to only two torpedoes, if I recall. He was returning from a mission and didn't expect any action.
Not actually returning, as it never reached assigned primary patrol area off Liverpool. Kaptainlleutnant Schweiger entered in his log, that, due to excess fuel consumption on the outward voyage, he had decided not to proceed North through the Irish Sea, but would patrol south of Ireland.
German Naval Command would learn this when the U-20 returned to port. I doubt they would then send a coded message.
So you have made my point entirely. There is no way this was “manipulated” by anyone, let alone Churchill. Hence, Germans=bad guys. Case closed.