Context. Giant radio galaxy (GRG) lobes are excellent laboratories for studying the evolution of the particle and magnetic field energetics and the past activity of radiogalaxy jets, as indicated by recent results of X-ray observations with Suzaku. However, these results are based on assumptions of the shape and extension of the GRG lobe electron spectrum. Aims. We re-examine the energetics of GRG lobes as derived by inverse Compton scattering of cosmic microwave background (CMB) photons (ICS-CMB) by relativistic electrons in RG lobes to assess the realistic physical conditions of RG lobes, their energetics, and their radiation regime. We consider the steep-spectrum GRG DA 240 recently observed by Suzaku as a reference case and we also discuss other RG lobes observed with Chandra and XMM. Methods. We model the spectral energy distribution (SED) of the GRG DA 240 East lobe to obtain constraints on the shape and on the extension of the electron spectrum 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 Sunyaev-Zel’dovich (SZ) effect expected in GRG lobes that is sensitive to the total electron energy density. Results. We show that the electron energy density Ue derived form X-ray observations can yield only a rough lower limit to its actual value and that most of the estimates of Ue based on X-ray measurements have to be increased even by a large factor by considering realistic estimates of the lower electron momentum p1. This moves RG lobes away from the equipartition condition toward a particle-dominated and Compton power dominance regime. We propose to use the distribution of RG lobes in the Ue/UB vs. Ue/UCMB plane as another divide divide between the different physical regimes of particle and field dominance and radiation mechanism dominance in RG lobes. Conclusions. We conclude that the SZ effect produced by ICS-CMB mechanism observable in RG lobes provides reliable estimate of p1 and Ue and is the best tool to determine the total energy density of RG lobes and to assess their physical regime. This observational tool is available with the sensitive high-frequency radio and mm experiments.