giantsfan3:
This is a reliable way to do it -- and draws hardly any power (actually negligible compared to the self-discharge of a Li-ion); remember that a microcontroller like on an Arduino processes the measurement (a few instruction cycles) in much less than a millisecond, and then goes to sleep, where the current draw is very close to zero.
My thought was that the energy savings would primarily come from the LCD being off. While the microcontroller can go to sleep as you described, while in use the LCD must either be on constantly or cycled on and off fast enough to appear to be constantly on to the human eye.