The LIS3DH 3-axis accelerometer specifies that it's supply voltage should be between 1.71 V and 3.6 V. For most applications, this just means you are using either 1.8 V or 3.3 V as your main rail. However, page 12 of the datasheet also mentions that the absolute maximum for the supply voltage is -0.3 V to 4.8 V. Given that it includes a negative voltage, I'm going to assume that this rating is the safe voltage range that can be applied to the VDD pins.
It does specifically mention that "functional operation of the device under these conditions is not implied", but could I safely operate this device directly and exclusively from a LiPo battery? 2.7 V to 4.2 V is well within the absolute ratings, but what exactly am I risking at this point? I'm also not the first one to be using these kinds of voltages (ST Forums Thread).
Before you ask, using an LDO doesn't make a lot of sense for my application due to the extra circuitry to facilitate a multi-voltage I2C bus and limited PCB real-estate. I didn't feel like it was strictly necessary to include detailed info about my application for my specific questions, but I'd be happy to provide it if needed.