Well, I have the hardware, so I tested OP's configuration. It didn't work for me either. Same OP's problem.
The cause is the I2C address we are using (0x27). That's not my LCD address, probably neither your address. It's 0x3F in my case.
I discovered it I2CScanner, a short sketch that lists all I2C devices connected at that moment. So, run it (with the LCD connected) and watch with Serial Monitor for the address of your LCD.
Then replace all references to 0x27 (like lcd(0x27, 16, 2)
) with your real address. Just change one value for the other.

This is I2CScanner
//
// Version 1
// 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.
// Version 2, Juni 2012, Using Arduino 1.0.1
// Adapted to be as simple as possible by Arduino.cc user Krodal
// Version 3, Feb 26 2013
// V3 by louarnold
// Version 4, March 3, 2013, Using Arduino 1.0.3
// by Arduino.cc user Krodal.
// Changes by louarnold removed.
// Scanning addresses changed from 0...127 to 1...119,
// according to the i2c scanner by Nick Gammon
// http://www.gammon.com.au/forum/?id=10896
// Version 5, March 28, 2013
// As version 4, but address scans now to 127.
// A sensor seems to use address 120.
// Version 6, November 27, 2015.
// Added waiting for the Leonardo serial communication.
//
//
// This sketch tests the standard 7-bit addresses
// Devices with higher bit address might not be seen properly.
//
#include <Wire.h>
void setup()
{
Wire.begin();
Serial.begin(9600);
while (!Serial); // Leonardo: wait for serial monitor
Serial.println("\nI2C Scanner");
}
void loop()
{
byte error, address;
int nDevices;
Serial.println("Scanning...");
nDevices = 0;
for(address = 1; 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("Unknown 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(5000); // wait 5 seconds for next scan
}