The sketch you have written is for fm's newLiquidCrystal library using the LiquidCrystal_I2C i/o class.
As knut_ny mentioned, there is a LiquidCrystal_I2C library available in the IDE library manager; however, it will not work the example code you have shown. So if you want to use the LiquidCrystal_I2C library from the library manager you will have to alter your code to use the constructor and initialization API functions for that library since they are different from newLiquidCrystal.
If you want to use fm's newLiquidCrystal library you will have to download that library and manually install it as it is not available in the IDE library manager.
That library requires a very specific installation that is not typical of the way libraries are installed since it replaces the LiquidCrystal library that comes bundled with the IDE.
Then, you must ensure that the i2c address and the PCF8574 pin mappings in the lcd object constructor match the pin mappings used on your particular backpack. If they don't match, then it won't work.
The LiquidCrystal_I2C library in the library manager does not require entering any PCF8574 pin mapping information. While the constructor for that library doesn't need pin mapping information, it still requires the i2c address.
One potential issue with that library is that it hard codes the pin mapping. If the hard coded pin mapping in the library does not match the pin mapping used on your backpack it will not work.
Alternatively you could use my hd44780 library package.
It includes a hd44780_I2Cexp i/o class that will automatically locate the i2c address and auto configure the pin mappings for the backpack. This makes it easier to use.
It can quickly and easily be installed using the IDE library manager.
You can read more about here: https://github.com/duinoWitchery/hd44780
The API is LiquidCrystal and LCD 1.0 API compatible - see the summary of API functions on the github page.
The library includes examples. See the examples for the hd44780_I2Cexp i/o class which is for i2c backpacks.
You will want to first run the included diagnostic sketch I2CexpDiag to test your i2c signals and the LCD module RAM. This will verify that the library is working correctly with your LCD h/w.
There are other examples that you can look at to see which includes you need, the lcd object declaration, and the appropriate API functions for initialization.