There were two marques of this name in Germany during the same period.
1. dLorenz (Stettin)
This was a scooter with a 211cc two-stroke engine built by Ing. Arthur Lorenz of Stettin-Braunsfelde, Dunkerstraße 5, 1921-1922.
Sources: Tragatsch p196, prawobrzeze.eu
2. Lorenz (Berlin)
Manufactured by the Lorenz Brothers, Berlin 1921-1924 and then by Lorenz, Wittig & Co. of Berlin, 1924-1925
The motorcycle was powered by a Lorenz 126cc two-stroke longitudinal boxer engine and used cast aluminum pistons. These were also marketed under the name Rapid. The engines were sold to other firms including Hüffer.
An image dated 1926 shows a Lorenz 998cc V-twin, but it is not clear whether it is by the Lorenz brothers.
Sources: GTU Oldtimerservice, motorrad-oldtimer-photo-archiv.de