I would be careful here:
Lr 3.6 does - as far as I know - not change the name of the catalog. So the catalog that is named "Lr2" might be your catalog the Lr 3.6 is using.
Open Lr 3.6 and go >Edit >Catalog Settings > General tab. It tells you the name and location of your current catalog.
Don't delete it.
i'm using LR 3 catalog so I think it will be fine. I am going through all
the previews to make sure they're all there though. The application had
become so buggy, it was unusable. I've reinstalled it but I want to clear
out anything that might be interfering. my computer is too old for LR4