Please refer the links below.This has been discussed on Forums and many websites.
You have to save Lightroom catalog on an External location(that must be accessed locally by both computers)
So sync in Real time is not Possible between two computer,though it can be done using Lightroom mobile on handheld devices(Phone ,Tablet)
Hope that helps
thank you-totally helps. it's a bummer but at least now i can save time by not continuing to try!