A theoretical investigation of the lowest molecular states of LuBr located below 41,700cm−1 in the 2S+1Λ(+/−) and Ω(±) representations when including the spin-orbit effects, has been performed through SA-CASSCF and MRCI calculations. Potential energy curves have been determined for 21 2S+1Λ(+/−) and 42Ω(±) molecular states in the range of 1.70 to 3.50Å and the spectroscopic constants (Re, Te, ωe and ωeχe) have been deduced. Transition Dipole Moments have been computed for various allowed ΔΛ=0,±1 on the same range of internuclear distances. In the case of the ground state and the two expected lowest singlet excited states (1)1Π and (2)1Σ+, a good agreement with the experimental results is obtained while new results are reported for the not yet observed 18 2S+1Λ(+/−) and 42Ω(±) states. A comparison with previous studies on the Lutetium mono-halides LuF, LuCl and LuI is presented, leading to trends in transition energies, equilibrium distances and dipole moments.