Q: Using an LSM6DS3 IMU with a LiPo battery power supply and LDO with Enable I am trying to build a circuit containing the LSM6DS3 IMU (Datasheet) to be powered by the Sparkfun 110mAh Lithium battery PRT-13853 (Datasheet).
According to the datasheet of the IMU, it is able to operate in a voltage range from 1.71 to 3.6V (page 23):

The battery provides a voltage between 4.2 and 2.8V (page 4):

Edit: according to another question, LiPo batteries should not really be discharged below 3.7V. That should not change anything for my question though.
This means the batteries voltage stays high enough IMU during the entire discharge cycle, but must be regulated down.
Given the low current consumption of the IMU, I thought about using an LDO linear regulator. Would the TLV755P be a suitable regulator? If not, what alternatives would be better and why?

A: LDO's are suitable for the use of batteries, but you are correct that the battery needs to be protected from overdrawing the voltage (low voltage condition).
The TLV755P has an enable pin that can be used to shut down the LDO at 1.28V (falling voltage).

simulate this circuit – Schematic created using CircuitLab
So if you do use an LDO make sure that it has an enable
Also, make sure you calculate the power dissipated
Power = Voltage drop x current through LDO
(The voltage drop is the battery voltage - LDO output voltage)
If its more than ~250mW then it would be a good idea to look into how hot the part will get.
