Am not sure if my answer meets your expectation. But, theoretically, you can estimate the physical properties (including density) of any compound using equations given in physical chemistry books. Usually there are equations that describe the expected density of a certain compound depending on some constants found in tables. I'll try to find you a publication which used such technique to estimate the densities and other physical properties of compounds totally by calculations.

http://www.sciencedirect.com/science/article/pii/S0040603111005090

http://www.sciencedirect.com/science/article/pii/S0040603111000050

http://www.sciencedirect.com/science/article/pii/S0378381213003257

Once you know both the lattice paramters (and angles) and the number of formula units per unit cell, it is straighforward.  From the lattice geometry and lattice parameters, calculated the volume of the unit cell.  From the number of formula units per unit cell (Z), you have Z times the formula mass: 6.9+58.3+32.0=97.2 -> 97.2(Z) amu per unit cell.  Divide the amu per unit cell by the volume per unit cell and you will have density in units of amu per cubic nm.  Then just convert units.

LiCoO2 does not possess a NaCl structure which is cubic. HT-LiCoO2 cell has 2 parameters: a (ca. 0.28 nm) and c (ca. 1.4 nm).