Interesting web site.
To answer Gordon's question about why they haven't caught on, I would say that the primary reason, Lyon's claims notwithstanding, is that the thing is in C. The clarinet literature is in Bb. Keep in mind that these are primarily targeted at young students: What is a student in a school band with a Lyon C supposed to do, play flute parts? Or is the band director supposed to transpose the clarinet parts for students with this clarinet? A private teacher may be willing to do this, but I doubt that many band directors would have the time or inclination.
Lyon's clarinet probably hasn't caught on for the same reason nobody makes C Melody saxes any more. It might be fun to play around with the thing at home, especially if you have a lot of piano music, but if you are going to play in an ensemble it could be a real headache, either for the player or the director.