I'm with Nogo in that using a file manager will be much quicker than importing all of the images to Lr and then moving them. The problem of course is that you have duplicate images, since you say many of these are backups. If you know that all of the duplicate images will have both the same filename and edit state, and the folder structure is also the same then it shouldn't be too hard. Simply drag a folder tree to the new drive and copy it across. For each drive you are using, just ensure that you place duplicate top level folders in the same location, but don't allow it to copy duplicates. This will ensure that if you have additional files in a folder on one drive, that are not on another you sweep up everything. That way you should end up with one copy of every folder, with one copy of every file.
You would need to keep the folder structure the same for those that are already in your Lr catalogue. Moving a whole folder structure and resyncing to Lr is pretty simple, just ensure that you have an image in the root folder of every existing drive that is used by Lr. Once you have copied the data to the new drive, delete the image from the root folder on the old drive. Then all you need to do in Lr is go to the drives root folder and do the find image process on the image. As long as you have find nearby images selected it will then find every image that is on that drive, and in the catalogue. Once you have those files as the target of the Lr catalogue you can then import the rest of your images to the catalogue, without duplication, or loosing any existing edits.
If though you have many drives, and lots of duplicate images, which will be at different states of edit, and or have different file names it gets a bit harder. If the new drive is large enough to hold all of the data that is on the collection of smaller drives then what I would probably do is in the first instance use Lr to move all of the images already in the catalogue to the new drive. If you move not copy you won't end up later with a whole load of duplicate images in your catalogue, but if you want to keep the old drives as is as a backup, you will need to copy the files back to the drives later. This tends to be a bit slow because it seems that Lr deliberately does a copy command, checks that the file has copied, then deletes the old one step by step. It also has to update the catalogue at the same time. Still at least this way you get your existing Lr catalogue images onto the new drive, and still correctly associated with the correct image file. After you have moved your Lr images you will need to copy all of the other files to the new drive using a file manager, but this time you will need to copy any duplicates too. After that this is the point where you would need to copy the Lr images you moved earlier back to the original drives if you want to use them as a backup.
At this point you need to import all of the non Lr images on the new drive to Lr. When you do this you will need to not check the don't import suspected duplicates option, you will also need to allow Lr to import JPEGs adjacent to RAW files This will allow you to import files with both the same file name and timecodes but in different locations on the drive. If in the first stage you had copied the files in Lr, not moved them, at this point Lr would import all of the Filename(1).xxx copies that this would have created. Not an ideal situation. If you then just view all images by creation date in Lr you can quickly scan in grid view for duplicate images and make appropriate choices about which ones you want to keep. It might also be a good time to consider a logical folder structure to help locate files easily on the disk, I use main folders by year, then folders by date, but if you shoot more often than I do it might be better to go with year, month date. Any other organisational structure I find is better done using collections groups, collections, and smart collections.
The least attractive option, but the one you would need if you can't fit all the existing image data on the new drive for sorting, will be to import all of the images to Lr in their current locations. Again as you import the images you will have to have ensure you import suspected duplicates and adjacent JPEGs. Again I would probably use a dated folder structure on the new drive. In this case you will either need to move the images to the new drive, which would be my choice. If you need to copy them, so you still have a backup, then it is important that as soon as you have copied the image to the new drive you remove it from the catalogue. Because you are in the process of removing duplicates, you must not create any new ones! This is the slowest option, but it is at least the most certain to get everything you want copied over actually copied correctly without duplication.
Although using your computers built in file manager program is going to be adequate for this task when working specifically with image files, or other Adobe file types I really like to use Bridge as my file manager. For file specific things like moving and copying it is as fast as the OS specific program. Bridge is also very good at displaying image files, and makes it quite easy to see both an image preview, and quite a bit of EXIF data, even when an image is not selected, or when you have multiple images selected. Bridge is now free to use for anyone, all you need to do is create a free Adobe account. So you can use it even if you are using one of the older perpetual licence versions of Lr, or even if you use something else entirely for your image editing. The other great thing about using Bridge is that it is pretty much identical on both OSX and Windows, so if you ever need to use both types of machine, you can have a common photographically based file manager program.