  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 Local Group (LG). Assuming the age of the Universe
and the Cosmological Constant according to the recent values from the Planck
CMB experiment, we find the mass of the LG to be M_TAL = (4.73 +- 1.03) x
10^{12} M_sun, which is 13% higher than the classical TA mass estimate. This
partly explains the discrepancy between earlier results from LCDM simulations
and the classical TA. When a similar analysis is performed on 16 LG-like galaxy
pairs from the CLUES simulations, we find that the scatter in the ratio of the
virial to the TA estimated mass is given by M_vir/M_TAL = 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)) x 10^{12} M_sun.
