A couple of possibilties. Go to LW's menu bar, Tools>Options>Shutdown & make sure it's NOT set for shut down to System Tray. Shutdown immediately is probably the best option here. Shutdown after transfers means it won't close down until all uploads & downlds have completed.

Go to Start menu, Settings>Start menu & task bar & make sure LW is not one of those on the list.

If LW is continually opening up & I certainly hope it's not, then see LimeWire continually Popping up every few seconds & also Opening at System Startup