Strange situation in making backup on an external disk

As the screenshot above shows, tonight, while trying to make a backup of the files on my Mac OS X, Version 10.7.5, Processor 2.4GHz Intel core i5, Memory 4 GB 1333 MHz DDR3 laptop computer, I got this strange message:

The item "Documents.zip" can't be copied because it is too large for the volume's format

Now, the file in question, as the home window shows, is 32.68GB, and, as shown in the window just behind it, the hard disk I'm trying to copy it onto has 191.58GB available, so it should fit. So what is the reason of this complaint? Is this linked to apple (Mac) or is it the Hard Disk, which is a LACIE disk? How can I overcome this problem, if possible, or raise the "too large for the format" threshold to at least 8GB, from the ~4GB it currently sits at?

And have I chosen the appropriate SX for this, and if not, which SE would be more fit?

I'm guessing that volume's format is FAT32 and you're trying to copy file bigger than 4GB. That's FAT32 limit. Check this for a reference.

As the first point of investigation, check what's the format of your partition. If it's FAT then that's the reason. Change it to exFAT, NTFS or native OSX.

So available free space has nothing to do here and can be misleading.