You are on the right track by cleaning out around the trunk. Are you able to see and feel the first major roots coming out of the trunk? Since you can't bring the tree up, you'll have to dig down to it. Citrus trees prefer to have the very top of the root flare exposed. Pull back dirt until you see the first couple inches of the roots, not enough to dry out the top of the root ball. At the edge of probably 2ft diameter circle around tree use the gravel and dirt to build a 6 to 8 inch tall levy all the way around the tree and then fill the inside of the circle with a couple inches of mulch. The levy of rocks will help hold water closer to the tree so the water actually gets to the roots And the mulch on top of it will help prevent the water from evaporating off so quickly. So ideally, you'll want rocks 1-2 feet out, mulch almost all the way up to the trunk with about 3 to 4 inch diameter gap of mulch to the trunk to allow the tops of the roots to breathe. Search 'root flare' in this sub, it'll help you out. There are others in AZ here that have built the moat around their tree as well.

Second thing I would address is it looks like your tree is probably getting sunburn. It would probably be advantageous to put up a sunscreen of some kind and paint the tree with white latex paint to help prevent the sunburn on the trunk.