How does one replace an adjustable back box lug?
I don't think you can replace the lugs. They're effectively T-shaped and the cross piece is thicker than the upright so that it can't be pulled out of the slot.

You're going to have to remove the old box completely and replace it with a new one.

The hardest part is going to be knocking the old one out without removing half the wall as it's been well plastered in. First remove any screws on the back. Then taking a reasonably thin cold chisel or old flat bladed screw driver dig into the wall around the box to remove a thin layer of plaster all around. When the box is loose, carefully pull it out.

The new box should fit nicely into the hole and the wall can be made good with a little filler.