By far, the greatest current draw, on an LCD, is the backlight.
If you remove Vcc, to turn the BL off, you would have to reinit it when you turn it on again.
At the start of setup(), you have
lcd.backlight(); // initialize backlight
This command is the one you use to turn the BL on. There will be another command which turns the BL off. Try
lcd.noBacklight();.
Fof