  This paper reports the tenth-order QED contribution to the lepton g-2 from
the gauge-invariant set, called Set III(c), which consists of 390 Feynman
vertex diagrams containing an internal fourth-order light-by-light-scattering
subdiagram. The mass-independent contribution of Set III(c) to the electron g-2
(a_e) is 4.9210(103) in units of (alpha/pi)^5. The mass-dependent contributions
to a_e from diagrams containing a muon loop is 0.00370(37) (alpha/pi)^5. The
tau-lepton loop contribution is negligible at present. Altogether the
contribution of Set III(c) to a_e is 4.9247 (104) (alpha/pi)^5. We have also
evaluated the contribution of the closed electron loop to the muon g-2 (a_mu).
The result is 7.435(134) (alpha/pi)^5. The contribution of the tau-lepton loop
to a_mu is 0.1999(28)(alpha/pi)^5. The total contribution of variousleptonic
loops (electron, muon, and tau-lepton) of Set III(c) to a_mu is 12.556 (135)
(alpha/pi)^5.
