Unfortunately, LR has a reputation for sometimes dropping the ball when doing file system manipulation with large numbers of files. Thus my recommendation is to do the actual file move/copy using the computer's OS tools.
Using Finder/Explorer, copy or move the desired folders to the new drive.
Using LR, in the Folders panel, select the top-most folder you moved, right-click, select "Find missing folder" or "relocate folder" as appropriate, navigate to the new drive location. (See DJ's link for details on this part.)