Density is listed in data sheets because it important for several reasons. A key factor is that lubricants are usually sold by volume, but many ingredient, manufacturing, and shipping costs are expressed in weight. Density is needed to convert weight to volume. From a performance standpoint density can affect pumping efficiency, the suspension of free water and particles, heat transfer, and is needed in some viscosity conversions. It is also used as a fast and cheap quality control test.
Polarity affects density and therefore to some extent density may give some indication of polarity, although I would not expect a clean correlation due to other variables. Polarity causes molecules to be attracted to each other and thereby packs more molecules into a given volume, increasing density. This can be seen in the density of various base oils with different polarities. PAO has no polarity, while Group I base oil has some polarity, diesters more, and POEs more yet.
Approximate Density of 5 cSt Base Oils
PAO = 0.82
Group I = .87
Diester = 0.91
POE = 0.99
In the lubricant ester family where polarity and densities vary greatly (0.86 to 1.01), I often used density as a factor in identifying the chemistry in unknown products.