I'm running two machines on one monitor and both have LR installed. A change to a file on one machine just changes the xmp file on the "primary" machine (that's where the RAW files are), so when I activate LR on the other machine the editing I did on the first machine are all there.
Also it doesn't matter which machine the edits are done on, because I "import" the files at their original location (I still find that term odd - importing files to another location).

