Good point Egg, haven't tested whether you can send lords of the Nights Watch to the Wall. What an oversight by me!
Will test it now, edit this post with result later.
Edit: Only managed to capture one of the several lords I "defeated" in battle, and of course I could not send him to the wall. Problem is that it was a lord I had already sent to the Wall before, so I can't be 100% certain on which part of the interaction prevents it, but it is safe to assume that you indeed cannot send people already at the Wall to the Wall. Silly of me.
Will test it now, edit this post with result later.
Edit: Only managed to capture one of the several lords I "defeated" in battle, and of course I could not send him to the wall. Problem is that it was a lord I had already sent to the Wall before, so I can't be 100% certain on which part of the interaction prevents it, but it is safe to assume that you indeed cannot send people already at the Wall to the Wall. Silly of me.