What are the units of the measurements that come out of an accelerometer?
On the LIS2DH, the 16-bit register paris OUT_X_H / OUT_X_L, OUT_Y_H / OUT_Y_L, OUT_Z_H / OUT_Z_L are left-justified, regardless of which resolution is selected. In other words, the 0x80 bit of OUT_X_H will be 0 or 1 indicating whether the X vector is pointing one direction or the other.

The actual physical units are determined in terms of the Full-Scale range (in CTRL_REG4[1:0] also called FS1:FS0). Note that they use the small "g" to indicate the force of gravity at earth surface, 9.8 m/s^2. (Not grams of mass.) When full-scale is set to 2g, the OUT_X_H bit 6 means 1g, bit 5 means 0.5g, bit 4 means 0.25g, bit 3 means 0.125g, and so on.

The resolution determines how many of the measurement bits are valid. In 8-bit and 10-bit modes, fewer bits are determined. The highest resolution mode only determines 12 bits, OUT_X_H[7:0] and OUT_X_L[7:4]. The unused sub-LSBs of OUT_X_L are 0.