I would like to upgrade the Apple OS to 10.8.3 (Lion).But can I still use VMWare Fusion 2.08?
If not I would have to buy new software for both VMWare and Windows.
OS X 10.8.3 is "Mountain Lion" not "Lion". 
VMware Fusion 2.8 will not work under OS X 10.8.3 and you'll need to upgrade to the latest, which at the moment is VMware Fusion 5.0.3.
You will still be able to use your existing Virtual Machine(s) however for better performance you'll want to allow the Virtual Machine(s) to be upgraded to the latest virtual hardware either when prompted or from within the Virtual Machine's Settings.