Results preliminary to exact Hartree-Fock calculations for cubic lithium crystals are obtained by a method recently developed by the authors. The ls core orbitals have thus far been treated as non-overlapping and fixed, but this limitation is not inherent to the method. The valence electrons are assigned to doubly-occupied Bloch orbitals orthogonalized to the core functions. All energy contributions are evaluated exactly. The results are qualitatively in accord with experimental data on the lithium crystal, and indicate the practicality of complete Hartree-Fock calculations at favorable computation times