Apple - Command-Control-Arrow beeps (plays alert sound) in Lion

I've found a nice workaround. Create the file ~/Library/KeyBindings/DefaultKeyBinding.dict with the following content:

<=10.10 Yosemite (Found on GitHub/Atom)

{
    "^@\UF701" = "noop:";
    "^@\UF702" = "noop:";
    "^@\UF703" = "noop:";
}

10.11 El Capitan through 10.15 Catalina (from Adobe/Brackets)
You'll need to create the ~/Library/KeyBindings directory first, and the @ and ^ characters are switched.

{
    "@^\UF701" = "noop:";
    "@^\UF702" = "noop:";
    "@^\UF703" = "noop:";
}

The beeping you are hearing in this context is not because those key commands are mapped to something but quite the contrary because they are not.

Typing an unmapped key command will result in an audible bell.

As you note Command-Control-Right in results in an audible bell in Mail.app. You will also note that Command-N results in a new message.

So here's a proof to confirm my assertion:

• Open System Preferences > Keyboard
• Select Keyboard Shortcuts from the pillbox at the top
• From the menu at the right choose Application Shortcuts
• Click the small + sign at the bottom left of the right panel
• From the Application pull down select Mail
• In the Menu Title field type "New Message" (no quotes)
• Place your cursor in the Keyboard Shortcut field and type Command-Control-Right
• Click Add

Now return to Mail and type Command-Control-Right. A new message will be created but if you type Command-N you will hear the audible bell. This is because Command-N is no longer mapped to anything. We replaced it.

So when you hear the audible bell it often means that you are trying to do something that is not possible (i.e. typing a key command that has no meaning for the current application).