Most likely Mauritius would lease Diego Garcia to the US, just like the UK did, hopefully while negotiating a much better deal for the Chagossians.
It is not at all clear to me what lies behind Britains reluctance to concede here. They know very well they did wrong – violating their own rules – lopping off the territory in the first place. What if there really isn't any conspiracy behind the EU stance here, what if they simply vote what they believe is right?