Assumption. LDC with 4 data lines. 4 switches connected to ground.
Add pull up resistors to the 4 data lines. 10k to 100k.
The PIC to LCD and the LCD to PIC data will not be effected by the pull up resistors.
When the LCD is not being updated, leave it not selected so it is not looking at the bus and it is not sending data.
Also leave the PIC in 'input' mode.
Add a 470 ohm resistor from a data line to the switch. The switch can only pull down 470 ohms.
A PIC can drive a pin high with the switch closed. The LDC might be able to pull a 470 ohm load high. (try 1k, 2.2k??)
The PIC and LCD can talk with a switch closed.
When the LDC is not selected, the PIC can see a high (pull up resistor) or a low (470 ohms to gnd).