I got some lm1117 because I want to work with some esp8266 modules and have other small projects in mind.
I also happen to have some 3.7v 18650's lying around.
But I just read a post that lm1117 have about a 1v dropout, which I believe means that whatever you feed the lm1117 will at least drop out 1v, which means I'll get max 2.7v if I connect a 3.7v to it.
So for these lm1117 my nearest practical source is 5v huh?
For powering an nRF24L01+ I just use a diode to drop about 0.6v from the LiPo. At full charge voltage the LiPo would be at 4.2v and with a 0.6v drop that gives 3.6v which is within spec for the nRF24.
I suspect the same system would work with an ESP8266.
Of course I am not drawing a lot of current through the diode - just enough for the nRF24 and the Attiny1634. I am controlling a small DC motor and the motor driver is fed directly from the LiPo.
You may need an ultra-low dropout regulator. The AP1117 is a common "low" dropout regulator, which just means
its a bit less poor than the 78xx series regulators. Ultra-low dropout regulators can be 0.1V or so (but
note the amount of dropout increases with load current for every linear regulator).
Parametric search on an electronics supplier's website is one way to identify suitable devices.
The alternative, if supply rail noise is not an issue, is a buck switch-mode regulator