Thanks for your quick response.
I now installed "Microsoft SQL Server Management Studio Express" and changed the settings to mixed authentication.
The error still occurs however the text changed to simply "Login failed for user 'lssqluser32'."
What now?
By the way the LS Managemente Console tries to log on to server: 127.0.0.1\sqlexpress
It exists, but during the installation I chose '127.0.0.1\whatsup' for the Lansweeper SQL Server.
Indeed is the 'lansweeper32' Database not in 'sqlexpress' but in 'whatsup'.
So I guess the default Server in the Management Console is wrong. But if I change it the error stays the same.