We revise the mass estimate of the Local Group (LG) when dark energy (in the form of the cosmological constant) is incorporated into the timing argument (TA) mass estimator for the LG. Assuming the age of the Universe and the cosmological constant according to the recent values from the Planck cosmic microwave background experiment, we find the mass of the LG to be M TAΛ = (4.73 ± 1.03) × 1012 M which is 13 per cent higher than the classical TA mass estimate. This partly explains the discrepancy between earlier results from Lambda cold dark matter simulations and the classical TA. When a similar analysis is performed on 16 LG-like galaxy pairs from the Constrained Local Universe Simulations, we find that the scatter in the ratio of the virial to the TA estimated mass is given by M vir/M TAΛ = 1.04 ± 0.16. Applying it to the LG mass estimation we find a calibrated M vir = (4.92 ± 1.08(obs.) ± 0.79(sys.)) × 1012 M.