The people who originally planted that tree are didn't take care of it. Citrus bark is thin and needs protection from the sun in Arizona. In a tree like that it comes form painting the trunk and any exposed main trunks white with either white wash or white latex paint. I suspect the damage is on the west and south side. That area of the tree is dead. It can no longer transport sugars from the leaves down to the roots and water and minerals from the roots up to the leaves. You have already added to the damage by filling in a hole in the tree. Generally that is a very bad idea. As long as a reasonable amount of bark is still intact on the other side of the tree it will survive. I would paint the rest of the intact bark to protect it from further sun burn and hopefully cooling the living surface and improve its vigor. I would remove any peeled bark since it is dead and can trap fungal infecting moisture and hide predator insects. Another problem I see is improper pruning. You grow citrus up and then allow it to grow back down shielding the trunk from the sun. Also the best and most productive part of the the tree is the lower eight feet that unfortunately plenty of people remove. The last thing of concern is the tree looks buried too deep. If true there isn't much you can do about that but it will severely shorten the life of the tree. Now that i have looked at the other pics you took I am concerned there is no part of the lower bar that is intact which means the tree is dead. It may take a couple of years depending upon how much nutrients are stored. But it will die. The advice to plant a new tree nearby is a good one if you own the place and are going to be there for years. Here is a link that might be useful: AZ Coop Exch. pubs citrus

Missing bark typically mean injury (recent or old) to the bark and/or underlying wood is dead. I don't see the orange you refer to. Can you take another image, perhaps at a different time of day?

Try the Citrus Forum if you get no traction here.

I'd let them grow two season and keep the best, one only branch. You can cut about half off but don't trim water sprouts the same currant season. My preferred way is to graft to smaller branches about thumb size...or cut back about half to 3/4 and graft onto water spouts the following year, scion will heal over the same season, not to worry about braking off and healing in a large diameter stock. Bark grafting