I don't have experience with Mac LC, but my OSX system has stuffit expander program. I believe it unpacks lha files. Maybe there is a stuffit program that works on your LC?
If you could unpack lha on the Mac, and you already are communicating between the two, copy lha to your c: directory on the Amiga.
I believe winzip will also unpack lha files. The long way would be unpack it on the pc with winzip. Email the unpacked version to yourself. Pick up the email with the Mac and pass it to the Amiga.
Can you share details on connecting the Amiga to the LC?