  Applying the sum rule approach, we investigate the energy of a soft dipole
motion in $\Lambda$ hypernuclei, which results from a dipole oscillation of a
$\Lambda$ hyperon against the core nucleus. To this end, we systematically
study single-$\Lambda$ hypernuclei, from $^{16}_{\;\,\Lambda}$O to
$^{208}_{\;\;\;\Lambda}$Pb, for which the ground state wave function is
obtained in the framework of Hartree-Fock method with several Skyrme-type
$\Lambda N$ interactions. Our results indicate that the excitation energy of
the soft dipole $\Lambda$ mode, $E_{sd\Lambda}$, decreases as the mass number
increases. We find that the excitation energy is well parametrized as
$E_{sd\Lambda}=26.6A^{-1/3}+11.2A^{-2/3}$ MeV as a function of mass number $A$.
