Do you have a part number or other specific information about "Board A" and its LCD?

Relative to a 12 MHz 805x-series MCU, LCD's are ultra-slow, hence should be quite simple to monitor. The typical character LCD module (if that's what you're using) uses the Hitachi HD44780 controller IC or an equivalent of that. That IC has a typical command execution time of about 40 microseconds, and some operations take longer. Additionally, some initialization steps are very slow, taking between 400 microseconds and 15 milliseconds, though they occur only once during initialization.

None of these operations are so quick that they couldn't be captured, interpreted, serialized, and transmitted by your board "C" to your board "B" where they'd be serially received, interpreted, and written to a similar LCD.

Now, if the task involves translating the protocol for a different sort of LCD, or other display, the task might become more difficult. Simply displaying it on a remote board that has a similar LCD to that on the original board should not be taxing.

If you simply capture D(7..0), R/w, RS, and E, the at the falling edge of 'E' you could even do it with a CPLD at each endm thereby involving no MCU firmware at all.

RE