Sending textual and nontextual data simultaneously across a serial port
The idea that sundry terminal programs can cleanly deal with binary data intended for your LCD simulator doesn't seem realistic.  Instead, look for a method to suppress the binary data when the Arduino isn't talking to an LCD simulator.

For example, during startup the Arduino could send some fixed text and a number to the host, and if the simulator is running, it would reply to the Arduino with some other fixed text and the 9's complement of the number.  If the Arduino doesn't get such a reply within a couple of seconds, it turns off LCD-simulation data transmission.