At this time Logic hasn't written a driver for the LQ057q3dc02 display.
Sharp has written sample software for the LH75401-10 that may contain the code you seek. The code is available from http://able.sharpsma.com.
Check under the LH75401-10 section and download the ABL, CSP and BSP. Unzip all of the software. Contained within I believe they do have an example driver for the display, or atleast some example code close enough to be of use.
Logic Product Development