  Ion mobilities of Lr^+ (Z = 103) and of its lighter chemical homolog Lu^+ (Z
= 71) in helium were calculated for the ground state ^1S_0 and the lowest
metastable state ^3D_1. To this end we applied the multi-reference
configuration interaction (MRCI) method to calculate the ion-atom interaction
potentials in the different states. The Gram-Charlier approach to solving the
Boltzmann equation was used to deduce the mobilities of the different
electronic states, based on the calculated interaction potentials. We found
that the zero-field ion mobilities are similar for the Lr^+ and Lu^+ ions. In
addition, the ion mobilities of the different states are substantially
different for temperatures above 100K. The relative differences between the
mobilities of the ground and excited states at room temperature are about 15\%
and 13\% for Lu^+ and Lr^+ ions, respectively, which should be sufficiently
large enough to enable laser resonance chromatography (LRC) of these ions.
