UV rays and high temperatures.
I don't know where to find transparent UV filters suitable for your application. Have you put the display behind a plastic material, or conventional glass window? Some kind of glasses can block partially the UV radiation.
LCD's are very sensitive to temperature. Moreover, the LCD to pcb connections are made of plastic materials that can be damaged with the high temperatures that there is possible to reach witch direct sunlight. Although the LCD temperature never reach the limit operating temperature, taking this temperature near the limit might result in a long term damage.
Regards