Thr Lillypad uses a 168V instead of a 168P. It runs on low voltage but doesn't have the extra power saving features of the Picopower device.
Also, their power supply is separate and generates 5v from a single AAA battery. It only runs down to 1.2v, even though a typical AAA battery can keep going down to 0.8v.
My preference is to run a 168P at 3.3v, and use 2 batteries in series to feed a switching supply that can accept an input voltage range of 1.6v to 3.2v. That should cover the entire useful life of the batteries, and by keeping it's output voltage down to 3.3v we can save a lot of power. The MCU's current drain is roughly the same as the voltage goes down, so when you multiply the voltage times the current you can see a significant power savings by running at a lower voltage.
The 168P can keep running all the way down to 1.8v, but the external interface circuitry will often prefer 3.3v. In today's world we can usually live with 3.3v instead of 5v if we choose our parts carefully.
Of course we have to consider that the max clock speed may be lower when operating at a lower voltage. But most battery operated devices can probably accept 4 or 8 Mhz instead of 16 Mhz. In fact, the operating current will also be lower at a slower speed so we'd probably want to run it around 4 Mhz. Since the MCU can be put to sleep most of the time that 4 Mhz speed will only apply while in the active full speed mode.
Maybe we can talk the designers of the Lileypad into updating their design to give a longer battery lifetime?