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 _ { \textrm { TA } \Lambda } = ( 4.73 \pm 1.03 ) \times 10 ^ { 12 } M _ { \hbox { $ \odot$ } } 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 _ { \textrm { vir } } / M _ { \textrm { TA } \Lambda } = 1.04 \pm 0.16 . Applying it to the LG mass estimation we find a calibrated M _ { \textrm { vir } } = ( 4.92 \pm 1.08 \textrm { ( obs . ) } \pm 0.79 \textrm { ( sys . ) } ) \times 10 % ^ { 12 } M _ { \hbox { $ \odot$ } } .