If LW is closed then it shouldn't be using any of your bandwidth. Check in Task Manager to see whether LW's properly closed... if there's a LW process running - end the process.

You can change your shutdown options within LW's tools > options > system tray. If you choose 'shutdown after transfers', LW will stay open until all of your uploads & downloads in progress finish. If you choose 'shutdown immediately', LW will close straight away & any uploads or downloads can't continue. If you choose 'minimize to system tray' then LW stays running.