Is that "Bill" you refer to, me?
If so the hd44780 library examples never reference "LiquidCrystal_I2C.h" (I assume you misspelled your header file name in your comment)
The hd44780 library for your type of device will use
Wire.h
hd44780.h
hd44780ioClass/hd44780_I2Cexp.h
If you get an error reporting something about "POSITIVE" missing / undeclared, it means your code is attempting use the LiquidCrystal_I2C i/o class of FM's newLiquidCrystal library but the IDE is pulling in a different library.
This is caused by having a "LiquidCrystal_I2C" library installed (there are several of those BTW) and either not having newLiquidCrystal library installed or having both LiquidCrystal_I2C and newLiquidCrystal installed.
This is because both LiquidCrystal_I2C and newLiquidCrystal both have a header file named LiquidCrystal_I2C.h
This means that even if you have newLiquidCrystal installed, you can still end up using the LiquidCrystal_I2C.h header file from the LiquidCrystal_I2C library instead of the one from newLiquidCrystal since the IDE will prefer to use a header file from a library in a directory name whose basename matches the name of the header file.
My suggestion is to install the hd44780 library and use the hd44780_I2Cexp i/o class. The library will give you a "plug and play" "it just works" out of the box experience since it can auto locate the i2c address and auto detect the pin mappings used between PCF8574 chip and hd44780 LCD.
It is faster with more features and better documented than any of the other lcd libraries.
It also includes a diagnostic sketch to test hd44780 LCDs that use i2c backpacks and will not have any library compatibility issues regardless of any other libraries that may be installed on your system.
--- bill