I'm not familar with that model and don't know how old it is, but you may be up against the bios rather than a filesystem issue. Some older machines have various bios limitations that choke on disks over some size, which can vary from (IIRC) 504mb to 8.4gb. Usually a bios upgrade takes care of this, so if you haven't already, check Lenovo's drivers for an appropriate utility.
Once you're upgraded, I'm guessing that you should be OK. However, if you still want to try formatting FAT32, go here
http://gparted.sourceforge.net/livecd.php
and download Gparted. Using Nero or what have you on another machine, burn a CD from the ISO file. Put that in your 560x CD drive and reboot. You'll be running a mini-Linux with Gparted, the Gnu Partition Editor. It will let you partition your drive any way you want, with any filesystem you want -- NTFS, FAT16, FAT32. Works a treat.
Don't forget to set the flags on your FAT32 partitions in Gparted. Once the partition(s) is/are made, right-click on the partition and click Manage Flags. The primary partition will probably need to be set Boot and LBA. If you use an extended FAT32 partition for part of the drive, it can be set LBA (not boot).
Hope this helps. However, others here with more direct experience with this specific machine may have better advice for you, so I defer to them.