Lilypad USB with ESP8266

Hi everyone,
I want to build a circuit which includes Lilypad Arduino USB, ESP 8266 Serial WIFI Module, and a Lilypad Temperature Sensor for transmitting Temperature values to a mobile phone via Internet. But i have some doubts to use them.
Firstly, when i looked datasheet of the wifi module, i realize it consumpt current between 135-215 mA, however Lilypad pins could give 40 mA output according to its technical specs. If i use a 3.7 V Lipo battery that satisfy this power consumption and wire ESP 8266 VCC and GND pins with + and - pins of Lilypad, is this cause a problem? If yes how can i achieve this problem?
Secondly, i don't know how i wire Lilypad USB and ESP 8266 exactly for transmitting temperature values. I search on web but don't find any particular example, especially there is no rx and tx pin on Lilypad so i don't figure out hıw i connect them.

I am a mechanical engineering student so i have no deep knowledge of electronics or communication but i want to learn, please explain simply as possible.

These are products i would like to use:

Thank you for your answers

You will need a 3.3V low dropout voltage regulator capable of at least 200 mA to power the ESP8266 from a LiPo battery. The regulator could also power the Lilypad via the 3.3V connection, if accessible.

For the USB Lilypad you will have to use some version of SoftwareSerial, none of which work very well. Consider using a different Lilypad.