I would suggest removing 1/3 canopy each year until you can stump it to a reasonable height--starting with that branch which is crossing over the other one. Citrus are susceptible to sunburn of the trunk and prefer to shade their interiors (thus closed canopy). On the 3rd year, when it is stumped where you need it, it will send vertical shoots. Let it. If it sends vertical shoots prior to this, prune them at about 6"-12" so they branch out and create shade instead of a sprout.
The 3rd year sprouts will shoot straight into the air way out of reach. This is what you want. If they produce oranges, the weight of the fruit will weigh down the vertical growth, and create a weeping branch that will become uniformly rounded and more prolific each year, while shading the trunk in its natural element. More importantly, do so at a height that is manageable for you to pick and not shade out your yard.
If the vertical shoots fail to fruit, then you can force the weeping mechanic by carefully bending them, and tying the tip off and staking it downward to train it in the proper fashion and mimicing the fruit weight and achieve the same thing. After a few years of this training, it will be a giant rounded ball instead of a massive shade tree, have stronger cold resistance, and because your fruits are closer to the ground, they will taste 3x better and pickable. Most of the fruit will grow under the guard of thick foilage as well, which will prevent much of your peel appearance issues.
The biggest mistake people make is trying to shape their citrus like a stonefruit (which benefits more from getting sunlight and air circulation on the trunk). Doing this will butcher the poor citrus tree and keep it stressed, burned, and unnatural. In almost ALL cases, pruning is only done to remove the dead, damaged and diseased branches--and occasionally crossing branches which may make contact at maturity and create an area for disease and pests. Outside of that, they are only pruned for "our" needs due to space, reach and accessibilty.