Arduino Mega 2560 RFID Serial Communication
First of all, try testing 1 functionality at a time to isolate the issue.
Now you do not know if the LCD is not working correctly, or if the serial communication with the RFID module is not working correctly. Connect it to a computer and test both independently.

When getting gibberish from a serial line, usually it means the baudrate doesn't match. Both devices have to send the same amount of bits per seconds in order to communicate with each other.

This is the Arduino example to test 2 serial lines (for Arduino Mega) at the same time: http://arduino.cc/en/Tutorial/MultiSerialMega