You could try cutting it back gradually until you find live wood and then see if it will sprout from there. Having said that, since it hasn't been thriving for awhile you should probably just discard it and plant new.

You could also start anew and put your currant tree to the side and it might sprout and you will have 2 trees. What kind of lime is it

It's a dwarf key lime

Go to your grocery store and buy a bag. The seeds will start producing fruit in 3 years. They will also grow better than a grafted key lime.

Steve

Is your lime tree grafted? If so, scratch test above the graft on the trunk to see if the lime is still alive, if it is green, then with proper care and assuming it isn't dying of a systemic disease, the tree should rebound. If the scion (the tree above the graft - in this case the lime) is dead,
then you'lll get rootstock citrus plant coming back from the roots. If it is a rooted cutting and the roots are alive, it can rebound (again assuming not diseased).

you may have a citrus disease infection or mineral salt buildup try putting it in fresh soil and remove all the dead roots but I'm no expert check with some one that knows what to do better than I

remove all diseased wood from plants and it will recover it looks like this time fertilizer not doing the trick but I'm no expert check with some one that knows citrus better than I