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To my knowledge you can't if one machine is already using the catalogue but once one has shut down then the other one will be allowed access to the catalogue with the edits.
I don't know if you could use LRViewer on one machine while the other is using the catalogue but wouldn't think so.
I was able to use one version of LRViewer across a network share, with LR closed on the target machine.
Haven't tried it recently, since the very strong recommendations from the dev team to avoid network access.
Aric, are you wanting to this in a professional environment, or a home setup? (I ask, because one of my continual hassles is managing my family's access to my images).
Another possible solution is to use DNGs, making sure to do metadata and preview updates.