Pseudopotential calculations of the ground state energies of the Lanthanum neutral atom, first and second corresponding cations by means of the variational Monte Carlo (VMC) and the diffusion Monte Carlo (DMC) methods are performed. The first and the second ionization potentials have been calculated for Lanthanum. The obtained results are satisfactory and comparable with the available experimental data. Studying the DMC energy of the La atom at different time steps, gave us a time step error of the order 0.0019 Hartree for the smallest time step, τ = 0.0001 Hartree^-1, and -0.0104 Hartree for the largest time step, τ = 0.01 Hartree^-1. This paper demonstrates the ability of extending the QMC method for lanthanides and obtaining highly accurate results.