  This paper reports the result of our evaluation of the tenth-order QED
correction to the lepton g-2 from Feynman diagrams which have sixth-order
light-by-light-scattering subdiagrams, none of whose vertices couple to the
external magnetic field. The gauge-invariant set of these diagrams, called Set
II(e), consists of 180 vertex diagrams. In the case of the electron g-2 (a_e),
where the light-by-light subdiagram consists of the electron loop, the
contribution to a_e is found to be - 1.344 9 (10) (\alpha /\pi)^5. The
contribution of the muon loop to a_e is - 0.000 465 (4) (\alpha /\pi)^5. The
contribution of the tau-lepton loop is about two orders of magnitudes smaller
than that of the muon loop and hence negligible. The sum of all of these
contributions to a_e is - 1.345 (1) (\alpha /\pi)^5. We have also evaluated the
contribution of Set II(e) to the muon g-2 (a_\mu). The contribution to a_\mu
from the electron loop is 3.265 (12) (\alpha /\pi)^5, while the contribution of
the tau-lepton loop is -0.038 06 (13) (\alpha /\pi)^5. The total contribution
to a_\mu, which is the sum of these two contributions and the mass-independent
part of a_e, is 1.882 (13) (\alpha /\pi)^5.
