Not sure I follow. So you want to open up debian bash and log into your nas? Isn't this the default option that you can do out of the box? Activate ssh on your nas and use a terminal command to log in? Such as a bash command line in your OS?
Only way I could see this happening is if there is a console/management port on the Synology NAS. Or Synology started to support USB peripherals and HDMI/other graphics connections. Or there is a terminal emulator run within a web interface.
Not looked into but guessing lxterminal provides some graphical interface to an emulated CLI that's access via browser. There must be some graphical environment in which it is running and browser is the only option for DSM.