I have some Lolin32 Lite boards which work off a 18650 battery. These batteries generally deliver 3.2V to 4.2V.
I think that the voltage is regulated through an AMS1117 3.3V.
What confuses me is is that the data sheets say that the dropout voltage for the AMS1117 is typically 1.1V. Therefore, to get 3.3V out, you would need at least 4.4V in. Which is greater than a fully charged 18650.
The dropout of the regulator will be smaller when the current drawn is lower. That 1.1V "low" dropout will be at the maximum rated current.
There are regulators with truly low dropout, such as mcp1700-33, ht7333, but they have a lower input voltage range and a lower maximum current, so choose carefully.