How generate a square wave from a DC voltage to power on LCD crystals?
To properly turn on the elements of an LCD you need a signal which has (on average) no DC voltage. So a clock and the inverted version of the clock would be a solution. The simplest way to make those I can think of is with Schmitt-trigger inverters:







simulate this circuit &ndash; Schematic created using CircuitLab

I select Schmitt-trigger inverters because then you only need a resistor and a capacitor to make an oscillator.

Note that you can also make a Schmitt-trigger inverter from other Schmitt-trigger gates like Schmitt-trigger NAND gates in a CD4093 chip.

The LCD elements must be connected between clk and clkn

You can also use an NE555 but then there's no inverterted clk signal.
A solution for that would be to make a 1/2 Vdd voltage using two equal value resistors. Then connect the LCD element between 1/2 Vdd and the NE555's output.