Connecting display to arduino
A guess that this display does not have a built-in controller (based on conector with a large number of signals).
It's easy to discover a "dumb glass" type display; It presents at connector HSYNC, VSYNC, CK and also R, G, B (for
colored). But there are some exceptions, as I will describe below. A complete display system needs 04 elements: (1)
Microcontroller / DSP / FPGA. (2) Frame buffer or memory. (3) Controller. (4) LCD glass. The task of the controller is continuously take the image data to be presented from the frame buffer and to activate the display signals properly. There are several combinations integration for these elements. For example, controllers with and without frame buffer, there are microcontrollers with built-in controller; microcontrollers with memory specific for images; some with everything inside, except the display; and even the most picturesque ones like an LCD with controller and also configurable as "dumb glass" (disregarding the internal controller).
   The size of the frame buffer will depend on the amount of colors associated with each pixel (color depth measured in bpp - bits per pixel).
For example, the memory needed to store a 320x240 screen  dots with 16 bpp (65K colors) will be 320x240x2 = 153600 bytes. Of course that, with less colors, less memory will be needed. 
   So, answering your question: Should be selected (an email to the manufacturer will be able to help you - application notes commonly shows some piece of code in C language, for initialization at least) an appropriate controller and, unless it has an integrated frame buffer, it will not be possible (or practical) to control this display with Arduino. Otherwise, if a controller is present, then you can use numerous libraries avaliable for this goal. This happens regularly with displays removed from smartphones and similar consumer equipments.  If you need fast screen changes and animations, all the more reason not to use the Arduino - low speed). Ideally, use 32-bit processors bits, with built-in facilities for color graphic displays.

EDIT

Apart from the exact identification of the LCD mentioned on question, I've included this edit in order to clarify only when discussing about LCD internal/external controllers and presence/absence of HSYNC/VSYNC signals on LCD module connector. The figures below show the internals of T-55343GD035JU-LW panel from Optrex when connected with a S1D13513 controller from Epson, generating the several signals for that LCD panel, including HSYNC and VSYNC. It must not be confused with internal "timming controller" of LCD panel (also highlighted in figure).