My comments assume the mouse has removed the cambium all the way around the stem. If not, the tree may recover on it's own.
If the lime is on it's own roots, or the mouse chew above the graft, it is likely that it will sprout below the chew portion.
If the tree is grafted, and damaged so that it cannot resprout, or if you just want to try to save the top portion, it may also be possible to bridge graft, or use some other grafting method to repair the damage. I have made smiliar grafts and they worked fine, but they were done when the plant was in active growth. I think such a graft may work when the tree is dormant too. It is worth a shot.