Hi there!
The first detail that would make a difference is whether you want the board to operate at 3.3V or 5V.
There is a linear regulator (MIC5219) on the board that regulates the input voltage down to 3.3V from an input. With linear regulators, the input needs to be a certain amount higher than the desired output. This difference in voltage is called the dropout voltage. I checked the datasheet of the regulator, and the dropout voltage is 0.35V, which means if you want a 3.3V board, the battery must have at least 3.65V.
I checked your battery, which is a 3.7V battery. As such, the board will operate at 3.3V, but not for a very long time, especially if you are drawing a lot of current from the board.
If you want the board to operate at 5V, then you will need to get a boost regulator to bring your 3.7V battery up to 5V.
To check the board voltage, there is a small area near the USB port that has too small pads. If those pads are connected with a glob of solder, then the board is a 5V port. If the two pads are not connected, then the board is running at 3.3V. You might also be able to check the back of the board if there are any other indicating markers.
Good luck!