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This paper reports the evaluation of the tenth-order QED contribution to thelepton g-2 from the gauge-invariant set of 2072 Feynman diagrams, called SetIV, which are obtained by inserting a second-order lepton vacuum-polarizationloop into 518 eighth-order vertex diagrams of four-photon exchange type. Thenumerical evaluation is carried out by the adaptive-iterative Monte-Carlointegration routine vegas using the fortran codes written by the automaticcode-generating algorithm gencodeN. Some of the numerical results are confirmedby comparison with the values of corresponding integrals that have beenobtained previously by a different method. The result for the mass-independentcontribution of the Set IV to the electron g-2 is $-7.7296 (48)(\alpha/\pi)^5$. There is also a small mass-dependent contribution to theelectron g-2 due to the muon loop: $-0.01136 (7) (\alpha/\pi)^5$. Thecontribution of the tau-lepton loop is $-0.0000937(104)(\alpha/\pi)^5$. The sumof all these contributions to the electron g-2 is $-7.7407(49) (\alpha/\pi)^5$.The same set of diagrams enables us to evaluate the contributions to the muong-2 from the electron loop, muon loop, and tau-lepton loop. They add up to$-46.95 (17) (\alpha/\pi)^5$.

Tenth-Order QED Lepton Anomalous Magnetic Moment --- Eighth-Order Vertices Containing a Second-Order Vacuum Polarization