I am creating an arduino alarm clock/light sculpture, but I can't for the life of me find any information about the lifespans of LCDs that are running 24/7 for a very long time. If anyone has any information on them, please tell me. Specifically, I am using this one.
The lifespan of the LCD and the electronics is just like any electronics part. When it is bad quality it will last a few years, when it is good quality it is more than 10 years.
A LCD watch from the 1970s might still work today. That is a few decades.
The backlight might get dim. That depends on the quality of the led and how bright it is set. The cheapest leds have only 50% brightness left after a few months. I suppose they didn't put the cheapest led in that display. I expect it to be okay for many years. Don't set it to the highest brightness. A resistor for the backlight of 220 Ω is common, you could start with 470 Ω and see if that is bright enough.
I see sometimes that the backlight display is directly connected to 5V, without resistor. If you have done that, then you have reduced its lifespan.
There are a few weak parts: The potentiometer for the contrast, the large capacitors on the Arduino board (if there are any), and the power supply.
If the display is more or less at the same room temperature, you could replace the potentiometer with a single resistor of 100Ω to 10kΩ from the LCD contrast pin to GND.