Unfortunately, and somebody may swoop in to correct me on this, I think Mac OS 10.6 removes most of the old appletalk features.

If you have a TCP/IP stack on the LC, your best bet may be to enable FTP on the macbook pro and use an FTP client on the LC III, or use AFP over IP, which you'd do by opening Chooser on the LC III, clicking on appleshare (I tihnk that's what it's called) and then clicking on "Server IP address" and typing the IP address of the macbook pro.