Hi, I have disassembled a Brick set that was broken, I have disassembled it to use the lcd screen, however I do not know how this works, it has zebra connectors, passing a male jumper to the connectors it shows random things, but I do not know how to connect them to the arduino to control what is shown.
Connect them to any suitable display controller, then connect the display controller to the Arduino. Use the Arduino library coming with the display controller for writing to the screen.
IOW: put the display on your trophy board and buy a display with controller and Arduino library.