The backplane signal is basically the common for the LCD display, so it's quite like the common cathode or anode of an LED display. The part about the LCD displays requiring higher voltage isn't necessarily the case, however. In most all driver systems I've worked with, 5 volts has been the supply voltage, sometimes it's as low as 3 volts. The current requirement for the actual display segments are often orders of magnitude lower than LEDs, eg. 10-20 mA for LEDs, where LCDs generally only require microamps (or less) per segment.
The main thing about driving LCD displays is that they must use an alternating (square wave) drive signal. DC is not used, as it will damage the display by electroplating away the microscopically thin, metallic electrical areas of the segment. Eventually, the display segment would stop functioning altogether.
You could certainly use a micro to control LCDs, but it may be easier to use a chip specifically designed to drive them.