I'm not sure about this because I don't use a Mac, but you should be able to share most processing by using the xmp metadata files. In the Library module, with the files selected, choose Metadata/Save Metadata to File, and it creates a "sidecar file" alongside of the image file. Once you move the files to the other machine and import them, execute the Metadata/Read Metadata from File to "get" the edits.
What this won't do is copy all of the library info, such as tags. To share that between two computers, you would have to actually move the library files to the other box. I don't believe the PC and the Mac could do that but I could be wrong. To share between two PCs or two Macs, by the way, you need to make sure that you shut down the first copy of Lightroom, because LR puts a "lock" on the library when it's open. Just sayin'.