The RK II has the 99.999 % of the Lonestar classic circuit. (well at least the sound).the LS is an awesome sounding amp. It compares quite favorably to a Fender Twin. IMHO, it sounds better than the Twin.
I had purchased a Lonestar classic, but after having played a RK II in GC two days straight for about 4 hours each day, I returned my LS and ordered a custom RK II.
)
BTW, I did not like the clean channels in the RK I when I tried it a few years back. Mesa fixed the only weakness this amp had. Now it is perfect.
If you're considering the RK II and are particularly interested in the cleans you should try the Lonestar to get an idea of the the cleans sound like in the RK II.
Just my .02