If you have selected the option for LimeWire to close immediately instead of going to the system tray it should close down and no activity should be able to take place.
I'm not sure about if you have closed Limewire to stay active in your system tray, but I think that if your computer has entered the sleep section that it is unable to continue downloading or uploading further files.
If your Internet connection is continuing activity after you have closed limeWire I would say there is something seriously wrong and it would be a good idea to let a technician have a look and see if you system has been compromised by a virus or trojan file. Before that I would run a good Antivirus over your system to check that it has not become compromised that way. If you don't have an AV program you are just asking for trouble.