I sympathize - I have several hundred asiatic lilies with the same issues. Just to get through a season requires daily picking off the red beetles and removing the leaves with the black stuff. I have some level of success with this, but after each summer of daily picking, I'm completely worn out. Most anti-chemical people recommend you do just that - picking off the beetles and black stuff. If you don't pick, the lilies are completely destroyed. If you vigorously pick, the lilies look okay, but never really good. I have never been able to get complete control by picking - maybe if I picked 3 times a day, but then I'd end up spending 8 hours a day bent over, and my aged back can't cope with that.
The beetles have, in my area, 3 cycles of about 20 or 30 days each. Even if you think you've picked off all the offenders from the lilies, a new round of the beetles appear before you know it.
Some people suggest the use of Neem oil if you can find it as a non-chemical control. I haven't used it yet, but am looking for the product. It doesn't work on the adult (red) beetles, so I imagine you have to spray the eggs or the black yuckie stuff. I believe you have to spray regularly especially since the beetles have cycles, so if you don't get rid of all the offenders, they come back for another cycle.
You can research on the internet, but there really isn't a "cure" for this. I have been slowly but reluctantly removing my lily patches because I just can't deal with the level of work attached to them. If you can stomach using harsh chemicals, I tried the chemical carbaryl this year. After the beetles came out and started laying eggs, I sprayed my remaining lily patches with the chemical (in my area, it was in the product "Grub Out"). That was about a month ago. I haven't seen anything since, but I fully expect that that I may have trouble as another cycle of beetles come out. For me, this is a temporary solution as I go about the strenuous work of trying to get rid of my lilies.
Check out the site: http://www.rcgardens.ca/factsheets/factsheets/neem.html
I love asiatic lilies, but there are lots of other beautiful plants that can be used instead that don't require such effort or the use of harsh chemicals. I'm moving over to the daylilies - not quite as vivid, but nice nonetheless.