I too have a lend lease pistols with British markings. The back strap of mine reads "POL.LUN.76" for Polizei Luneberg Waffe 76. Luneberg is a town in Northern Germany. These were used in West Germany after the war. It sounds like it was used in two different towns after the war, hence the "Old.779" and the "LUN.487".
Since lend lease guns were not required to have all the british proof marks during the war, yous, like mine, was sold after the war and that is why it contains all the proof marks, and the markings "Not British Made" on the right side of the frame in front of the trigger guard.
I hope this answers some of your questions. I'm sure someone else on the forum will have more to say.