Three Li coin cells, what an odd (no pun intended) number of batteries to use. Wonder what batteries they are (CR2016, CR2032, CR2025, etc)? I’m guessing they must be in parallel, otherwise if in series my guess would be that it would overdrive the LED and thus require a current limiting resistor – which would be a waste. In parallel, there would be great battery life and the internal resistance of the Li coin cells would inherently limit current flow and prevent the LED from burning out. However, this arrangement, base upon my experience with other Mfrs “microlights” would only work for longer wavelength LEDs (red, orange, yellow/amber) as their forward bias voltage is within the range of a single Li coin cells typical voltage. Shorter wavelength LEDs are “doped” differently (as are white LEDs) and so have a higher forward bias voltage (the voltage needed to get the LED to switch on and produce light) and normally two batts are put in series – still with no current limit resistor necessary for the same above stated reason).
Very curious design. Are you sure that it is not two or four batts? What color is the LED? What is the battery numerical designation (e.g. CR2016)?