Using an LSM6DS3 IMU with a LiPo battery power supply and LDO with Enable
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 &ndash; 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.