This has been annoying me on my work with Lightswitch, great tool for building business applications. Finally I found this information on a forum. It didn't get a high score there, but it was spot on.
With you want to change the connection strings in debug/release mode, search for Web.Config in project tree under the ServerGenerated folder. There you will find the connection string that is used by Lightswitch in design time.
You will have to close and reopen the solution so the change takes effect...
Thanks to Nehemiah Willis post at: Original forum post