CAS-SCF/MRCI calculations have been performed for nine molecular states in the representation (2S+1)Lambda((+)) (neglecting spin-orbit effects) for the molecule LaF. The corresponding 20 molecular states in the representation Omega((+/-)) (including spin-orbit effects) have been calculated using a semiempirical spin-orbit pseudopotential built up for lanthanum. Calculated potential energy curves and spectroscopic constants are reported. To the best of our knowledge they are the first ones from ab initio methods for the excited states of LaF. Comparison to recent experimental data display a good agreement with averaged discrepancies DeltaT(e)=95 cm(-1), DeltaR(e)=0.033 A, and Deltaomega(e)=5 cm(-1). Predictions are provided for the new triplet transitions under investigation in our laboratory involving the excited state (2)(3)Pi as well as for the yet unobserved state (1)(3)Sigma(+).