There are some technical issues:
- Adafruit_INA219 is hardcoded to use the Wire library.
- The Arduino.cc Wire library for AVR based boards that comes bundled with the IDE does not support changing the pins used.
You can run both the INA219 and the lcd on the same i2c bus using the Wire library, but depending on how the pins are mapped, it may not allow you use all the analog pins.
I'm not sure which board you have and how the i2c pins are mapped.
One thing that may help is if you run the I2CexpDiag sketch that is included with the hd44780 library.
It will print out information about your board and the i2c pins used by the Wire library.
--- bill