You could use the same cable and RJ45 to connect the keypad and your UNO to the LCD. At 5v levels with no differential signalling using just simple twisted pairs like in Cat5e or CAT6 you could probably get 10ft or so sending serial data at 9600bps. I personally don't think you will have any issues with 1 ft. Just be sure you pair the transmit and receive with a signal ground in each.