I have checked the Wemos schematics and the input voltage regulator at 5v pin convert the voltage to 3,3V and the minimum input voltage for this regulator is 2,2V, so in consequence with 3,7V it will work fine :)
This is something that I want to check (currently I'm waiting by the slow Chinese boat xD with my components).
In theory with the battery and the charger you will get a voltage around 3.7V at the battery output so I don't know how will work the 5v voltage regulator only with 3,7V. Instead...