  The recent discovery of the gamma-ray emission from the lobes of the closest
radio galaxy Centaurus A by Fermi implies the presence of high-energy electrons
at least up to gamma ~ 10^5 - 10^6. These high-energy electrons are required to
interpret the observed gamma-ray radiation in terms of inverse Compton emission
off the cosmic microwave background (IC/CMB); the widely accepted scenario to
describe the X-ray emission of radio galaxy lobes. In this Letter, we consider
the giant radio lobes of FR II radio galaxies showing that it is possible to
maintain electrons at energies gamma ~ 10^5 - 10^6, assuming an acceleration
scenario (driven by turbulent magnetic fields) that compensates the radiative
losses. In addition, we consider the contribution to the diffuse extragalactic
gamma-ray background due to the IC/CMB emission of FR IIs' lobes showing its
relevance in the keV to MeV energy range.
