I²C LCD long distance

Long distance wires with I2C over those kind of distances would be tricky, there would likely be high line capacitance. I2C is more suited for short range intra-board tasks.
You could use the serial UART port on the Controllino, run it at say 4800 BAUD and use a serial to I2C/SPI board such as the one here: https://www.sparkfun.com/products/retired/9981

You could try the i2c at those distances and run it at its lowest speed. nothing to lose by doing that I suppose.