During the 1900 Army Test Trials, many guns were submitted, both autos and revolvers. Among these were the Luger, submitted by the firm of Ludwig Loew & Co., agents for DWM.
The original Luger was in .30 Luger, and at the Army's request, a new cartridge was hurriedly made up for it, a 9mm round. By 1906 or so, only the Luger and Colt remained in competition. The Luger was in strong competition, but the Army was not about to accept another small bore, stinging from the adoption of the .38 revolver previously. So, the Army asked DWM for a .45 specimen.
DWM complied, making up about a dozen models in .45 caliber. Impressed, the Army asked for 100 .45 caliber Lugers for field testing. By this time Loew and DWM were fed up and dropped out of competition.
The German Navy adopted the Luger in 1902 in 7.65, and the German Army adopted the 9mm in 1908. England authorized it in 9mm about that time also, as did Switzerland.
Incidentally, 9mm Luger ammunition of the time was loaded with a flat point, truncated cone bullet. It is identical to the 9mm Glisenti round, and can only be distinguished by ammunition labels or headstamps. The 9mm Parabellum was never produced in Italy (at that time) and the 9mm Glisenti was never produced in Germany.