The 68LC040 was a mutation of the Motorola 68040
line of chips. While the 68040 was (is) rather widely applied, the 68LC040 (as far as i'm aware) was only used by Apple
The only difference between a 68040 and a 68LC040 was that the 68LC040 didn't have an FPU. This made it cheaper. It also made it kind of suck. Since most people couldn't tell the difference, and the 68040 was the first chip apple used that had a built-in FPU anyway, slashing out the FPU to save cost probably made sense from their perspective, but it was still obnoxious.
The name comes from the fact that the 68LC040 was originally designed for use in some of the later computers in the Macintosh LC line, specifically the LC 475 and LC 575. It was also used in a number of lower-end Powerbooks and almost all of the early Performa line (the only computers apple ever put out that were even dodgier than the LCs).