Oh, I think I understand now, you are using the LED driver as a port expander to feed the inputs into the LCD?
One simple approach would be to create/use a library that allows you to turn on/off each pin on the LED driver.
Then modify the LCD driver of your choice, by replacing the pin on/off calls with calls to the library to toggle LED driver pins.
If wanted to get fancy, could think about how to use PWM functions, but timing might be an issue (unless you have enough control of the PWM that you can get several channels to output a synchronized wave-form.)
You might also look at how people have handled using a shift register (e.g.) as a port expander for running LCD on Arduino.