I removed LDO from my NodeUSB (ESP8266) board, and use LiFePO4 battery to power it directly.

700 mAh able to run about 6 hours (345 minutes):

2016-07-08 13:04:30.324560

2016-07-08 18:50:05.973346

Then, I charged LiFePO4 battery (3.3V LDO directly) and ran another test:

2016-07-08 23:40:50

2016-07-09 01:15:34

That is 95 minutes, so about 27% of capacity, 190 mAh.

Second test is much batter (I charged longer this time, for 3 hours):

That is about 47% of the capacity.

If use 3.5V LDO to charge LiFePO4 battery, it can reach 95% of capacity. I will test it next week.