Awe, you're not failing Lincoln at all...You're the reason he's done as well as he has! I can't imagine what condition he'd be in if anyone else was his owner...seriously.
I was reading through the latest replies, and the only thing I can comment on is that yes, I think adding humidity to his environment is a good idea to try and see if it helps...But what people need to keep in-mind is the environment that Lincoln lives in, Colorado...It's basically the same as my environment in central PA right now, it's cold and very dry...And a bath does not equal humidity! That's why I recommended not bathing him more than once a week, because it's going to just make his already dry, itchy skin much, much worse. I know they come from a "tropical" climate, but that is a climate that is humid, not cold and dry as all-hell. I can speak from personal experience, I sell cars for a living, and this time of year my hands just start cracking to pieces because of the dry cold. And it's so much worse after I shower and go outside, or even just wash my hands, dry them, and then go outside...So that's the reason I said to limit his bathing, and to at least try the Vitamin E oil after his bath. Adding humidity to the room he's in with a humidifier is a great idea, but that's totally different than bathing him, which could make the issue all the more worse, if that is the issue. Obviously his CAV thought that he had a dry-skin issue to recommend the Vitamin E oil, so that could very well be the entire issue he's having right now, the sudden drop in temperature and the dry air that comes along with it has just made his already dry skin much worse...
As far as your question about trying a "UV light" or "Full-Spectrum light", there are a million different takes on this question, but there are two things I can tell you for sure: #1.) You absolutely don't want to use an artificial light of any kind to lengthen his days at all, because that's just going to make his hormones much worse; his light-schedule should be the same as the Natural Light Schedule in your area, so if you were to buy an artificial light, you'd only want to use while the sun is up....and then #2.) There are a million different types of artificial lights, and when it comes right down to it, the only type of light that is possibly of any good at all is a "UVB" light, as this is the light spectrum that increases their body's production of Vitamin D, which in-turn can have a positive effect on skin and feathers both...When you hear the term "full-spectrum" light, that just means that it emits UVB light along with UVA and UVD, along with producing heat as a by-product, and these are basically worthless, without going into detail.
What is most-important about choosing an artificial UVB light is that is has a high-enough UVB output that it will make a difference, and then that it is safe and does not emit any harmful light-rays along with the UVB. It's a good rule to always stay away from any artificial UVB bulb that is a Coil/Spiral bulb, because they are the most harmful/dangerous ones, as they emit some very harmful light-rays that are a by-product of the manufacturing process used to make them...The Coil/Spiral UVB bulbs are the ones you hear about causing blindness and skin damage/cancer. The other thing about Coil/Spiral UVB bulbs, just the same as Compact UVB lights (ones shaped like a regular lightbulb and that fit into a regular lightbulb socket) is that neither of them, in-general, emit a strong enough UVB light to make any positive difference at all. The only Compact UVB light bulb that has a useful UVB light output are the Mercury Vapor Bulbs, however these are "all-in-one" bulbs that also emit UVA light and heat in addition to the UVB light. So while there are some very good Mercury Vapor Bulbs out there when it comes to their UVB output, they are also going to emit a good amount of heat as well, which is probably going to be counterproductive if dry-skin is an issue for Lincoln.
The only totally safe and effective UVB lights are the long, UVB tube lights that fit into strip-light fixtures. The two strengths of UVB tube-lights are T10, and then the much stronger T5 tubes. Both emit a good amount of UVB light that is totally safe, but the T5 UVB tube-lights put out enough UVB light that they are comparable to actually having him out in natural sunlight; they also last a lot longer than the T10 UVB lights (all of them, whether tube, compact, or coil/spiral), as the weaker T10 UVB lights must be replaced at least every 6 months, depending on their output level, while the T5 UVB lights only need to be replaced once every year. There are a lot of different UVB output levels, but the most effective and still safe are the 10.0 UVB bulbs (they come in 2.0, 3.0, and 5.0, all of which are weaker than the 10.0)...So in-short, the most effective UVB light that is also safe would be a 10.0 T5 UVB tube-light. They only need replaced once a year, they emit no heat or dangerous light rays, and they have a strong enough UVB light-output that the bird is actually getting enough UVB light to make a difference if he is able to be underneath it for at least a few hours a day (and the T5 tubes are strong enough that they don't have to be close to the light-tube either, which also commonly causes eye and skin damage)...The question comes down to "How beneficial is this going to be for my bird?"
That's where things get fuzzy...Birds are not like reptiles, they don't require an external source of UVB light for their bodies to produce Vitamin D, nor do birds need an excess amount of Vitamin D in order to absorb the nutrition from the food that they eat like some reptiles do. Birds work the same way we as people do as far as this goes. As long as they are eating a healthy diet that provides them with the proper vitamins, minerals, amino acids, etc., then they don't need excess UVB light to provide them with nutrition, nor do their bodies necessarily use the extra UVB light for much at all. Yes, if they get no UVB light at all, just like people, they can start to develop certain Vitamin Deficiency Diseases, but assuming that you don't lock your bird in a closet all day long and you don't feed it junk, then the benefits of putting them under an artificial UVB light are minimal at best. And because people don't understand what they're buying or know much about the different types of lights, a lot of people buy bulbs that are actually very harmful to their birds, even if they keep the bulb at a good distance from their bird.