Hi @hendrik.kuehnel ,
Auth0 will default to just one user/password database connection, so in your case its current default is Database 1. To connect with Database 2 the connection parameter needs to be specified in the /authorize call, hence why its falling here when a user that belongs to DB 2 attempts to sign in.
So your applications may need to handle how it points the user to the right connection to use. Alternatively I think it possible to write some logic when using Auth0 Lock that could determine which database to use, see further information here - Select from Multiple Connection Options.
Thanks!