The completely unexplored LaP molecule is investigated by ab initio methods.Potential energy curves for the lowlying states of LaP are constructed by means of the diffusion Monte Carlo method combined with three different trial functions.Spectroscopic constants are also numerically derived and the ground state is assigned,looking forward to experimental comparisons.Moreover,variations of the permanent dipole moments as a function of the inteuclear separation for the two lowest states of the diatomic LaP are studied and analyzed.