I had a project at one client where a 4 row by 8 column LCD was not powering up correctly. We fixed it by using a small PNP transistor to switch the power ON to the LCD well after the microcontroller was up and running.

Hook the PNP up as follows:

Emitter of PNP to the Vcc (+5V most likely).
Collector of PNP to the Power Lead of Display module.
Base of PNP to 10K resistor.
Other side of 10K resistor to 8051 port pin.
It is also a good idea to add another resistor of 47K between PNP base and PNP emitter.

Before LCD Init time the software drives the port pin low to enable power to the LCD module. Wait a short time for the LCD power to stabilize. Then proceed with normal controller initialization.

Michael Karas