On one of my pi builds that does broadband speed testing and has a 20x4 LCD I that I loan out to people with broadband speed issues, i simply put up a final message that says "Please wait 30 sec before powering off good bye"
how are you ending the program that does the writing to the LCD ?
can't you add the back light off command to that program so that when you exit it the last thing it does is turn off the back light.
If you really want to power the back light only on shutdown, you could modify the LCD so the the back light is controlled by a transistor, you can then bias the base low normally and on power up you run a python program that drives the base high turning on the back light, then on shutdown all outputs would switch off resulting in display being off.
We want information… information… information........................no information no help
The use of crystal balls & mind reading are not supported