In June 1935, Lüdke was promoted to Generalleutnant and took command of the 9th Infantry Division.

After the death of the commanding general, Wilhelm Knochenhauer, he was assigned to the leadership of X Army Corps.

On 1 June 1940, Lüdke was appointed commander of German troops in Denmark where he replaced Leonhard Kaupisch.

His time in Denmark was relatively peaceful, and it was only towards the end of his period in command that the Danish resistance movement was becoming increasingly noticeable.

After the Telegram Crisis, Adolf Hitler wanted a harder line implemented in Denmark and Lüdke was deemed unfit.