LCD Display connection
That display requires you to send each frame as a frame in its entirety.  You need to send the full pixel data for each and every pixel with all the right timing.  Kind of like driving a VGA monitor.

While it is possible to do it with a generic microcontroller, that microcontroller must:


Have enough RAM to store the entire frame buffer
Be fast enough to generate the clocks and data streams while still leaving you enough processing time to do what you want to do.


There are specialized microcontrollers that have extra hardware in them to specifically drive this kind of display.  The one I have used in the past is the PIC24FJ256DA210.