In my experience with lithium batteries, the 3 wires are connections to battery terminals and to protective thermistor. If you find a battery in the right size and have electrical abilities you can generally make it work but if you lack stop here since lithium batteries can burn crazy. Thermistor value will be typically off compared to original, but you can bring it within the range with a resistor in parallel or in series to the original. I have not tried moving the thermistor between batteries, but this is presumably doable. Testing the operation of the thermistor is advisable. Finally, people have also given up on the thermistor, but I do not see a good reason for doing that other than laziness. Again, you are playing with literal fire.