The original Pebble uses a Sharp LCD. The Pebble Time uses JDI display. I have no idea what display the Time Round uses: do you know for sure it's a Sharp unit?
I'm not positive they still use the Sharp brand, but I'm pretty sure the display technology is the same: LCD backed by SRAM in the display. You don't need to continuously update the display. Once you write a frame or part of a frame, the processor can go to sleep.