Since I had a bout of HLLE on my emperor angel several months ago, I have done a lot of reading about this disease. There are many claimed causes of HLLE including, of course, carbon. However, I cannot find any authoritative publications that demonstrate this to be true. I strongly suspect that HLLE is a symptom of any one of a number of problems, including carbon, stray voltage, etc. That is, all of the claims may be true under a particular set of circumstances. I "cured" the HLLE in my fish by making water changes and adding additional vitamins to its food. I already had a grounding probe in the tank, and didn't use carbon. The fish got better, but I can't really claim that anything I did caused the improvement. Physicians know well that most human diseases get better given time, and that probably also applies to fish.
All of that said, in response to your question that started this thread, I agree with MichaelTX - the best filter is ls and lr. I haven't used an additional filter in 15 years, and have had good success with FO and reef set ups.