Saving masked photo in lightroom

This is a common misunderstanding. You have created a mask, and now you are looking at the image while you have selected a mask overlay that makes the non-masked background white or black, thinking you have changed the background this way. That is not the case however. The mask overlay is not an edit, it is just a way to see what is masked and what is not masked. When you leave the mask tool, the mask overlay is switched off and the image returns to normal. That is why you think you still need to 'save the edit' somehow, but you didn't make any edit.

If you want to turn the background black, then you will have to mask the background and then use the sliders in the mask panel to get the effect you want. Setting the Exposure to -5 may make the background dark enough to consider it black, but if that doesn't do it then you may need to go to Photoshop which is the better tool for this kind of edit.