I am using Lego Mindstorm Block from Dexter to get data from arduino board moisture sensor and control turning on/off a led attached to arduino. I work perfectly fine.But it EV3 stop communicating arduino once I add in a 20x4 I2C LCD display. The LCD connectied with the same A4 A5 GND VCC pins with EV3. Please help. Thanks.
If the Arduino is connected to the EV3 through I2C, the EV3 will act as the I2C bus master. The EV3 does not support multi-master I2C (at least not without advanced understanding and specific control to prevent collisions). If you need to use an I2C device with Arduino, you either need to implement the drivers on the EV3, or you need to use a different I2C bus.
You could potentially use a bit-bang I2C bus on any two available arduino digital IO pins, and use that bus to interface with the I2C device.