Calculations of the pressure-volume isotherms for FCC La have been carried out up to pressures of 2 Mbars and temperatures up to 3.4 eV, using the self-consistent linear-muffin-tin-orbital method. The isothermal bulk modulus shows an anomalous stiffening over the pressure range 320-560 kbars, due to termination of the 6s to 5d electronic transition. The effect is calculated to be most pronounced at zero temperature and is largely washed out by a temperature of 3.4 eV. These results lead to a temperature-dependent peak in the lattice Gruneisen parameter, based on a simple Slater-model analysis. Hugoniot calculations using this Gruneisen parameter are in good agreement with experiment and reproduce the anomalous stiffening observed in the shock compression data for La. While the authors also find both significant overlap of the rare-gas cores and melting to occur in the vicinity of the shock anomaly, the present calculations identify the principal cause of the anomaly observed in the La shock data to be the termination of the 6s-5d electronic transition in this material.