The LC II has an 030. However, as some have pointed out, the architecture of the board is far different on the LC III.
An LC III needs an enabler to run, meaning it must use System 7.1 or later. You won't find the code necessary to support the machine in 7.0.1 or any version of 6.
Your best bet for running 25MHz System 6 is to use a Mac IIci. Accelerators for the LC and LC II may work but the drivers may require System 7, so watch out. (Note that the LC can run System 6.0.6, 6.0.7, and 6.0.8 while the LC II can only run 6.0. 8) .