Lcd Serial-IIC-I2C y mi mega

Hola, puedes probar con mi librería: https://bitbucket.org/fmalpartida/new-liquidcrystal/wiki/Home, en la sección de download puedes bajar la última versión.

Prueba con este código:

#include <Wire.h>
#include <LCD.h>
#include <LiquidCrystal_I2C.h>

#define I2C_ADDR    0x3F  // Define I2C Address where the SainSmart LCD is
#define BACKLIGHT_PIN     3
#define En_pin  2
#define Rw_pin  1
#define Rs_pin  0
#define D4_pin  4
#define D5_pin  5
#define D6_pin  6
#define D7_pin  7

LiquidCrystal_I2C	lcd(I2C_ADDR,En_pin,Rw_pin,Rs_pin,D4_pin,D5_pin,D6_pin,D7_pin);

void setup()
{
  lcd.begin (20,4);
  
  // Switch on the backlight
  lcd.setBacklightPin(BACKLIGHT_PIN,POSITIVE);
  lcd.setBacklight(HIGH);

  // Position cursor and write some text
  lcd.home ();                   // go to the first line, first character
  lcd.print("SainSmart I2C tester");  
  lcd.setCursor ( 0, 1 );        // go to the 2nd line
  lcd.print("It's Working!");
  lcd.setCursor ( 0, 2 );        // go to the third line
  lcd.print("Sainsmarts docs suck");
  lcd.setCursor ( 0, 3 );        // go to the fourth line
  lcd.print("Nice LCD Though. ");
}

void loop()
{

}

Por otro lado, como te comentan, necesitas conocer la dirección I2C del dispositivo, si no funciona cambia 0x3F por el valor que te de el siguiente programa:

// --------------------------------------
// i2c_scanner
//
// This program (or code that looks like it)
// can be found in many places.
// For example on the Arduino.cc forum.
// The original author is not know.
//
// This sketch tests the standard 7-bit addresses
// from 0 to 127. Devices with higher bit address
// might not be seen properly.
//
// Adapted to be as simple as possible by Arduino.cc user Krodal
//
// June 2012
// Using Arduino 1.0.1
//

#include <Wire.h>


void setup()
{
  Wire.begin();

  Serial.begin(9600);
  Serial.println("\nI2C Scanner");
}


void loop()
{
  byte error, address;
  int nDevices;

  Serial.println("Scanning...");

  nDevices = 0;
  for(address = 0; address <= 127; address++ ) 
  {
    // The i2c_scanner uses the return value of
    // the Write.endTransmisstion to see if
    // a device did acknowledge to the address.
    Wire.beginTransmission(address);
    error = Wire.endTransmission();

    if (error == 0)
    {
      Serial.print("I2C device found at address 0x");
      if (address<16) 
        Serial.print("0");
      Serial.print(address,HEX);
      Serial.println(" !");

      nDevices++;
    }
    else if (error==4) 
    {
      Serial.print("Unknow error at address 0x");
      if (address<16) 
        Serial.print("0");
      Serial.println(address,HEX);
    }    
  }
  if (nDevices == 0)
    Serial.println("No I2C devices found\n");
  else
    Serial.println("done\n");

  delay(8000);           // wait 8 seconds for next scan
}

Buena suerte.