Is it feasible to run the LPC1788 at 1024x768 at 24bpp? Or, does the bus width mitigate the maximum resolution at 24bpp and/or maximum color depth at 1024x768?

You can run up to 1024x768 at 24bpp as long as the bandwidth can be maintained by the LPC1788 and the DMA doesn't underflow. Unless you're driving that display size at a very low refresh rate, that specific configuration may not be feasible, as the bandwidth requirements will be higher than the LCP1788 can maintain. We offer a bandwidth calculator to help figure out if a specific configuration will be viable.