There is no need for a UV system in an outdoor residential pool exposed to sunlight. The only thing that UV will do better than chlorine is inactivate the protozoan oocyst Cryptosporidium parvum, but that is virtually unheard of in a residential pool unless you invite strangers over who have diarrhea.

As for a low chlorine level, you appear to be under the mistaken belief that the Free Chlorine (FC) level represents the active chlorine level. That is simply not true. When Cyanuric Acid (CYA) is present in the water, most of the chlorine is bound to it and effectively inactive. At the recommended FC/CYA levels in the Best Guess Swimming Pool Chlorine Chart, the active chlorine (hypochlorous acid) level is roughly the same as with only 0.1 ppm FC and no CYA.

Commercial/public pools with no CYA, such as many indoor pools, are essentially vastly over-chlorinated. That leads to people thinking that they need a low FC level to avoid problems, but the rate of oxidation of swimsuits, skin and hair, the rate of corrosion of equipment, and the rate of creation of disinfection by-products are all related to the active chlorine level so are lower by an order of magnitude (a factor of 10 or more) than in pools managed according to the principles of this forum.