  The triple differential cross section of
$^{208}\rm{Pb}(^6\rm{Li};\alpha,\rm{d})^{208}\rm{Pb}$ elastic Coulomb breakup
is calculated using the semiclassical method. We fit the parameters of the
Woods-Saxon potential using the experimental $\alpha-\rm{d}$ phase shifts for
different states to describe the relative motion of $\alpha$-particle and
deuteron. In order to check the validity of the two particle approach for
$\alpha-d$ system we apply a potential model to describe the
$^2\rm{H}(\alpha,\gamma)^6\rm{Li}$ radiative capture. Our results for the
Coulomb breakup of $^6\rm{Li}$ show large value of the forward-backward
asymmetry of the $\alpha$-particle and deuteron emission around zero energy in
the $^6\rm{Li}$ center-of-mass (c.m.) system. Comparison of the results of our
calculation with experimental data gives evidence for the dominance of the
Coulomb dissociation mechanism at the $\alpha-d$ relative energy larger than
$E_{\alpha\,d}>300\,\rm{keV}$ and sufficiently big contribution of nuclear
distortion at $E_{\alpha\,d}$ near zero energy, but essentially smaller than
the value reported in Ref.[F. Hammache et al. Phys.Rev. C82, 065802 (2010)].
