A secular determinant for the determination of vibration frequencies of lithium has been set up by Launay's method which takes the electron gas into account. Theoretical elastic constants have been used in the calculation of the force constants. Frequencies have been calculated for 47 points of the first Brillouin zone which gives the value of 3 x 1000 = 3000 frequencies by symmetry. Specific heats have been calculated by numerical computation in the range 300 to 6$^\circ$K and show good agreement with the experimental data. The agreement below liquid-air temperatures is surprising in view of the known phase transformation of lithium.