We have measured the energies and the Zeeman splitting of excitations of the non-ionized Li acceptor in CdTe by means of far-infrared absorption spectroscopy in order to determine the valence band parameters of the host material (0<or=B<or=7T, B//(100) and B//(110), 1.5K<or=T<or=4.2K). We have studied in detail the splitting of the G line (1S₃/2( Gamma ₈) to 2P₃2/( Gamma ₈)) using polarized light; g factors for initial and final states are given. Shifts of the transition energies caused by interactions with phonons are identified and separated by a critical comparison of the excitation energies measured for Li with results published for other acceptors in CdTe. Using the recently developed theory of Schmitt and co-workers, a set of valence band parameters of the host material is obtained, which reproduces very well both the excited acceptor states at B=OT and the Zeeman patterns. With a value of the static dielectric constant epsilon =10.31 taken from the literature the Baldereschi-Lipari set amounts to mu =0.68, delta =0.13, R₀=30.9 meV. The Luttinger parameters are determined as gamma ₁=4.14, gamma ₂=1.09, gamma ₃=1.62 and kappa =0.46. We compare these numbers with results obtained by different methods and published previously in the literature.