I wasn't talking about the schematic of the radio; I assume that's not available. I only meant the schematic of the part of the circuit built by you. Is it already working, or are you still in the planning stage?
If you want to switch between the LCD being controlled by either the radio itself or the Arduino, something as simple as an SPDT or 2xSPST will work, yes. The problem, however, is if you disconnect the display from the radio and then reconnect it without toggling the radio on/off, likely the display won't work. It's likely the display is only initialized on startup by the radio. On the Arduino side you have control over this, but not on the radio side.