FYI, if you're building this from scratch rather than using a battery manager -- battery impedance rises as voltage falls, so there comes a point when you can't maintain output power. This is important for switching supplies, which increase input current as input voltage falls, to maintain a regulated output.
That's apparent from the discharge curves, though it may not be obvious or explicit. Simply, the curves drop away that much faster, at higher currents, whether you've been drawing a high current or not. It's a state-of-charge thing.

I built a flashlight from scratch, using
discrete circuitry, and added a low-input-voltage throttle for this reason. Indeed, in my case it was not only nice to the battery but a required function, as the control circuit is also powered from the single cell, and if the control browns out, the whole circuit is... not very happy!

Tim