NodeMCU minimum supply voltage)
The NodeMCU uses the SPX3819 3.3v voltage regulator.

That regulator, according to the datasheet has a dropout of maximum 700mV, but much less at lower currents.

Taking the maximum, that means that you need to supply 3.3 + 0.7 = 4V to the board for the regulator to regulate properly. However, it is doubtful you will be using that much current, so probably nearer a 350mA dropout - which means 3.3 + 0.35 = 3.65V.

However, the ESP8266 itself will work down to 2.5V - so if you operate the board with the regulator out of regulation (not recommended, but it should work fine), you could probably go as low as 2.8 to 3V without problems.