Most important: Do not apply Vee when VDD is off. Vee without VDD causes latch-up and this will burn the driver ics.
To avoid remaining charges on the LCD, Vee should be turned off before stopping the driving signals. But this is often hard to do when power is switched off externally and is ignored in most designs. Modern LCDs are quite robust.
The easiest solution: Generate Vee out of VDD and do not use excessive capacitance at Vee, then it should be ok.