You should check closely the data sheet for the controller chip used on your LCD module. Almost all of the controllers I have worked with have capability to support either parallel or serial. Many have a P/S mode selection pin and in the serial mode the pins that were D6 and D7 become the clock and data of a serial interface.

Some manufacturers of graphic LCD modules, particularly the chip-on-glass (COG) types, save pin count in the connection cable by not making the P/S mode pin available at the interface. So look at BOTH the controller data sheet and the module spec sheet.

Note that the common D6/D7 type of controller serial interface only supports write cycles to the display controller. This means that if you need to support adding additional pixels into existing display bytes then it will be necessary to have a local RAM buffer image that mirrors the display content.

Michael Karas