LCR is the film standard, LRC is the SMPTE standard. The difference was designed to confuse everyone and foster many debates about which is correct. I think LRC was developed to maintain consistency with stereo formats, with the first 2 tracks always being LR.
No one has been able to sufficiently explain this to me so, for HDcam masters, I ship my tracks L,C,R,Ls,Rs,Lfe. And subsequently, no one has ever called me to tell me I'm a buffoon.
Perhaps some of our other members can shed some additional light. I'm interested, as well.