Systematic local density treatment (via the all-electron, full-potential, linear combination of gaussian orbitals fitting function (LCGTO-FF) algorithms) of the cohesive properties of mono- and dilayer Li when combined with recent calculations for bulk Li of similar high quality, yields a prediction of modest intraplanar lattice expansion (dilayer: 2.8%, monolayer: 1.6%) and substantial interplanar contraction (dilayer c/a=1.46 versus calculated bulk c/a=1.64). The differences between these predictions and the limited experimental data for Li overlayers on graphite (which exhibit about 6.1% expansion in nearest-neighbour separation) suggest possible substrate or bonding effects in the experiment. The total dilayer cohesive energy is 79.8% of the bulk cohesive energy while for the monolayer the fraction is 63.1%. The interplanar contribution to the dilayer cohesive energy is -0.29 eV. The dilayer uniaxial (c-axis) compressibility is 2.5 times as large as the calculated value for the HCP Li crystal (the latter value is in quite good agreement with available measurements). Mono- and dilayer energy bands (at the level of bare Kohn-Sham eigenvalues) are basically consistent with those calculated self-consistently for the crystal using the same LDA model. However, calculated work function values are larger than measured crystalline values, by more than 0.6 eV, for both the mono- and dilayers.