Parallel vs Serial
When you use LiquidCrystal library you have to tell it the GPIO pins that are used to connect to the display. There are two control connections and a 4-wire parallel data connection.
However, the LCD display on your E-term communicates using a TTL-level serial link, not a parallel GPIO link.
Easy to use LCD display and Keyboard decoder combo that integrates with any controller circuit. The LCD can display up to 80 alphanumeric characters at a time in 4 lines x 20 characters arrangement. The keypad consists of a 0-9 numeric keypad and 6 user defined function keys. Communication with the host is via serial port operating at TTL level.
You can't drive your E-term using LiquidCrystal library.
Your diagram is small but it shows TX and RX connected to the Eterm, not a set of 6 GPIO pins.
Note that, in most Arduinos the same TX and RX are used for USB communication with the Arduino IDE software on your PC. To transfer compiled sketches to the GizDuino+. So you may need to switch the RX connection between USB and E-term somehow. AT least disconnect RX from your E-Term when using the IDE to program the GizDuino+.
The E-term description says
Power Input: 8-12V
Display : 4x40 LCD
Input device: 0-9 numeric keypad and 6 user defined function keys
Note that it requires a minimum of 8V. Your diagram shows the E-term Vin connected to the GizDuino+ Vin pin. This wont't supply 8V if you are powering your Gizduino from the USB 5V supply. You need to power the combination from an off-board supply of between 8 and 12 volts (e.g. 9V 1A wall-wart or battery)
- Ensure the E-term has it's 8-12 V supply connected to a supply of that voltage.
- Set the serial comms speed to the data rate in the E-term manual.
- use Serial.print() not LiquidCrystal.print() etc.
// initialize the serial communication:
// send text to E-Term
void loop() // run over and over again