HI,
why not use Digital Potentiometer from Maxim etc.
For -Ve supply for LCD also Maxim good.
OR Opamp with inverting mode, dual supply and input with PWM (from uC) and resistor-capacitor filter to generate -Ve at output.
there was a application note on microchip.com that demonstrates +12v to +170v. If you put inductor in (-) line you would get -170v. I didn't read the article but i think switching time of fet specifies outpul voltage.
hi .. i am using and pwm from avr and some op amps to control contrast
of my lcd via software. If you need higher voltage try icl or maxim 7662 .. it is voltage inverter/doubler in small size and low cost
If I remember correctly, Maxim makes a power supply chip that is a boost/invertor with an external digital up/down control. I have used it, but many years ago.