According to the documentation for 7.0.x, the newest LC series with the 68LC040 cpu has an issue with the built in floating point processor and will not work.
However, the LC iii is listed as working with the 68030 cpu. Minimum specs state 8MB ram and 60MB disk space if you want to do something more interesting than boot.
I am currently trying to figure out the best way to install on my IIci, as I only have a floppy drive. If you have CD rom or card/usb adapter that might be an easier way to install.
Possibility of installing over ethernet via booting from floppy?
Kind regards,
Jay