Cough cough.....
There is no technical maximum, it varies according to the type of cable but I would not recommend more than about 10cm with CAT-6 cable. The wires are twisted pairs which in an unbalanced system like an LCD will create havoc with the signals, the cable capacitance and inductance is also far too high.
If the LCD has to be positioned remotely, you need to use a more appropriate link, for that distance. You stand almost zero chance of carrying TTL level voltages at relaively high speed. A better idea would be to use a serial link to send the data and some 'intelligence' (=MCU) at the LCD end to recover it and format it for the LCD module to use. Given the relatively slow speed an LCD works, you should be able to do it over a simple RS232 link at modest Baud rate.
Brian.