Sliding lug on backbox has sheared off, is it possible to just replace a single lug?

You can buy them. They even fit on the back box where or if it’s a fixed lug.

If its the adjustable lug you can most often replace those. The fixed lug you cant and would require replacing the back box. An old temporary fix i was taught when working for the council (surprise surprise) was to drill through the back box, put in a raw plug and put in the center of the raw plug a length of cut rawplug to fill out the plug in the wall. If done correctly, this allows you to temporarily fix the issue with a longer m3.5. The larger issue then becomes the fact that faceplate fixing then is not earthed to the back box and if discovered during a periodic inspection will be flagged up. I'd personally change the back box just to avoid causing another issue further down the road, do it once, do it right!

This is possible to do, if it’s a fixed lug drill a small hole in the back box and then use a 3.5mm tap to then thread the hole for the 3.5mm screw this then complies with earthing. Another option is to buy back box repair lugs which are relatively new to the market. Better still would be to remove the back box and replace with new.

If you find your local CEF wholesaler they sell a socket lug replacement kit. Easy to install and good fix done properly.