Yes, That's what this is, a 1920 commercial model where the Weimar government had the Great War markings removed. I would never find a Luger in this condition for the price I paid if it were a 42 (Nazi) marked gun or even a WW1 marked gun.
Actually, that's not entirely correct.
Commercial Lugers were meant to be sold commercially, as such, they did not have any of the military markings to start with. DWM manufactured commercial Lugers from 1900 until 1918, right along side military and various contract Lugers. Almost all Commercial Lugers are in .30 cal (7.65mm x21). In 1908 The German Imperial Army rubber stamped the Luger and called it Pistole 08 (aka P.08), but they required it to be made in the new (at the time 9mm) Parabellum. So all German military issue Lugers were 9mm.
In 1918, after the Treaty of Versailles, Germany/Wiemar Republic made an effort to reclaim all the war time armament, and millions of guns (handguns and rifles) were destroyed between 1918 and 1921. Some guns, including a lot of Lugers collected during that time were stamped on top of the chamber with a 1920, right next existing manufacture date. These are the so called double date models, however, the 1920 is not really a date, rather it's a Property mark, showing the gun was reclaimed by the the Wiemar government. Since Germany's army was effectively dismantled these guns were sometimes modified for Police use, and other small government officials. Sometimes in 1921, DWM restarted manufacturing commercial Lugers, and continued to do so until 1930. During this period, they started to add a letter suffix to the serial number, and these guns became known as the "Alphabet Commercial Lugers".
In 1930, Mauser acquired all of DWM tooling and spare parts for the manufacturing of the pistol, and started making commercial and contract guns through out the 30's until 1942. Most of the commercial Lugers of this era have the Mauser banner on the toggle, unless they were made for a special contract. In 1933/34, Germany began rearming in secret, and Lugers were manufactured with the 'secret code" S/42 on the toggle until 1940, when they switched to byf. Most had the manufacture date stamped on the chamber, but some have date codes like the K (1934) and G (1935) K dates.
But enough history for now. There are many books one can pick up on the history of the Luger, with tons of information to help collectors.
My point is that if your Luger is in .30 caliber it was not official military issue, it was made for commercial use. If you can post some detailed photos of the front of the frame and bottom of the barrel, also both sides of the frame and barrel, top of the chamber and top of the toggle, I may be able to give you more information.
FWIW, I have 1937 S/42 Mauser Luger in 9mm, and I also have a 1917 DWM LP.08 Artillery Luger (my grail Luger). Guess which one is the shooter.