  Giant radio galaxy (GRG) lobes are excellent laboratories to study the
evolution of the particle and B-field energetics. However, these results are
based on assumptions of the shape and extension of the GRG lobe electron
spectrum. We re-examine the energetics of GRG lobes as derived by inverse
Compton scattering of CMB photons (ICS-CMB) by relativistic electrons in RG
lobes to assess the physical conditions of RG lobes, their energetics and their
radiation regime. We consider the GRG DA 240 recently observed by Suzaku as a
reference case and we also discuss other RG lobes observed with Chandra and
XMM. We model the spectral energy distribution of the DA 240 East lobe to get
constraint on the shape and the extension of the electron spectrum in the lobe
by using multi-frequency information from radio to gamma-rays. We use radio and
X-ray data to constrain the shape and normalization of the electron spectrum
and we then calculate the SZ effect expected in GRG lobes that is sensitive to
the total electron energy density. We show that the electron energy density U_e
derived form X-ray observations yields only a rough lower limit to its actual
value and that most of the estimates of U_e based on X-ray measurements have to
be increased even by a large factor by considering realistic estimates of the
lower electron momentum p_1. This brings RG lobes away from the equipartition
condition towards a particle-dominated and Compton power dominance regime. We
use the distribution of RG lobes in the U_e/U_B vs. U_e/U_CMB plane as a
further divide between different physical regimes of particle and field
dominance, and radiation mechanism dominance in RG lobes. We conclude that the
SZ effect produced by ICS-CMB mechanism observable in RG lobes provides
reliable estimate of p_1 and U_e and is the best tool to determine the total
energy density of RG lobes and to assess their physical regime.
