I don't think citrus are shallow rooted. They do have surface feeder roots that can be damaged by hoeing weeds. Too much water will cause tree roots to spread out on the surface and not grow deep but that is when planted in the ground, not in a pot.
Even if you don't repot, get rid of the saucer. Put the pot on a solid surface with something under the pot edge to keep it from sitting directly on the ground. That will help the pot drain faster and also keep creepy crawlies from moving in.
Cut all the dead wood out of the tree.
All that new growth will be tender and very sensitive to cold damage. It sounds like your temperatures are good right now but I wouldn't leave your plant outdoors when the night time temps starting getting into the 30's.
