Voltage Supervisor for low battery
If batteries are improperly treated, they can puff up, heat up, and outgas. This sometimes leads to fires if the battery is big enough. It is important for all batteries to measure for undervoltage, overvoltage, under/over current, and improper temperature. I generally recommend using a specific battery supervisor to deal with what you can.

There are so many cheap ICs specific to battery monitoring and it generally saves you battery lifetime as well. The IC can do a great job of stopping battery drain after the cutoff as well as giving the proper conditions during charging. This comes a little down to if the charger also needs to be on the device, but if not, there are very small devices for protection without charging(look at QLCSP packages).

You can use a micro for battery monitoring, and in fact it is becoming more common, but I won't use one for more than monitoring temp. What happens when your micro gets too low in voltage and the battery keeps draining? What about when your code hangs for sampling? There are also cases where there is a short under the micro and current draws from the battery at well over the specified discharge rate. Lithium batteries can only be discharged at generally 1C. Sometimes .5C and sometimes up to 2C. In these cases you want that separate IC to be your buffer.