I'm powering an attiny45 from a lithium ion battery; using these batteries the voltage cannot get below 3volts or it will damage the cell. How should I go about cutting the voltage out? Software, or hardware? I'm not sure!?
Holding the MCU in reset is both a decent way to reduce its current consumption to almost nothing as well as indicate that the battery is low. Unfortunately most ATtinys have 2.7V as their closest BOR value so you will require an external voltage monitor if that is not high enough for your purposes.
You will want to add a chip such as a TCM809T to your design. This chip will monitor the VCC line for being between 3.04 and 3.11 volts. When below that range an output pin will be driven low. You can use the output signal to control a FET voltage switch to cut off the load from the battery.