The splitting fruit syndrome and lack of juice/flavor is a sign of lack of proper irrigation. As all citrus trees are surface rooting, they benefit from a deep organic mulch to retain water, and regular periodic summer irrigation in areas without any summer rain. I would also suggest that you feed your trees several times during the warmer months to encourage more and sweeter fruit.

As to your lemon, are you sure you and your neighbor have the same type of lemon? Different cultivars fruit at different seasons and choosing the best cultivar for you conditions can make all the difference. Here in California, the Lisbon lemon is the best adapted to hotter climates, and can bear some fruit all year, mostly in fall. The Eureka is very similar in fruit, and is the most commonly sold type in markets here. The best and sweetest lemon for nearly year round fruit is the Dwarf Improved Meyer, but some people think it is too sweet to be a proper lemon. This one does best as a small container plant, or if you need lemons year round. If you like your lemons huge, look for the Ponderosa variety, these can get to be the size of grapefruits. I suspect that you will also have other varieties available to you that are not common here in the USA.

I have never seen leaf miners on Citrus trees. Here the biggest problems are probably snail damage, aphids spread by argentine ants and resulting in the sooty mold on foliage, keeping ants out of the tree will help control this, and whitewashing the trunk base really does seem to help control this. Lemons are also very prone to getting scale here, which is also spread by ants. A light dormant oil spray can really help control this problem, and is relatively non toxic to other things.

If you can create a berm to allow for a good periodic soaking of your citrus, and perhaps repeat this every couple of weeks in the hottest months, along with a deep mulch, or provide drip irrigation, you should have both healthier trees and better fruit. Aged chicken manure or horse manure ought to work very well.

Is it OK to prune orange trees? I have been unable to get rid of the soot that covers them and most of the fruit falls off the trees before it's ripe. I thought if I cut them back radically and soaked them and the surrounding earth in fungicide, I might be able to resolve the problem.