When using a Raspberry Pi and an LCD to run the printer, can the LCD controller that comes on the printer be removed or does it need to be used also?
No, when you run the print jobs from a Raspberry Pi, e.g. using the OctoPrint print server, you do not need the display of the printer as you can control the printer from the Pi screen or from a browser of any other device. Do note that not all functionality of the LCD controller is built-in in those printer servers, but you normally have a terminal to interface using G-code with the printer, or you can make macros to do that.
In some cases it might be handy to leave it on the printer for small adjustments, homing an axis, or feeding some filament; it saves you some time opening a browser to control the printer when you operate the printer remotely and allows to troubleshoot the machine manually.