The 8080 is not a microcontroller, but a microprocessor, so it had no special provision for LCD displays, as modern microcontroller may have, except maybe for the ability to use packed BCD numbers. It had no in-built host peripherals that would support protocols like RS232 or SPI.
You don't mention what kind of LCD display your college used, so this is only an assumption (and your question may be put on hold precisely due to the lack of information about this) but for the most basic LCD display, a 7-segment display, the software may have used BCD for storing numbers. That way, a number could be easily output from the data bus (8-bit parallel) to a latch "listening" in a I/O port. The output of that latch could be feed a BCD-to-7 segment converter/driver, with in turn would be connected to the display.
So, the protocol would have been 8-bit parallel (the 8080 data bus) with strobe (the signal generated by the address and bus cycle decoding , that is used to open the latch). This would have been work like this:
First, the current machine cycle must be decoded in order to know whether it is a I/O operation, memory operation, stack, instruction fetch, etc. The 8080 didn't have special pins, like the Z80A, to inform the system about the nature of the machine cycle. Instead of that, the 8080 used the SYNC pin to signal the beginning of a machine cycle, whose type would be encoded in the data bus during the time SYNC is active. The 8080 chipset included a machine cycle decoder, the 8212 controller, that was connected to the 8080 as this:
Now the hardware designer would have to use a 8-bit latch whose enable input would be triggered by certain value present in the lower part of the address bus (or most frequenctly, triggered by having a certain value in some bit of the lower address bus), and the WR signal and the OUT signal from the 8212. This 8 bit value, if packed BCD coded, can feed two 7-segment displays to show two digits.