  Energetic electrons in the lobes of radio galaxies make them potential
sources for not only radio and X-rays but also Sunyaev-Zeldovich (SZ)
distortions in the cosmic microwave background (CMB) radiation. Previous works
have discussed the energetics of radio galaxy lobes, but assuming thermal SZ
effect, coming from the non-thermal electron population. We use an improved
evolutionary model for radio galaxy lobes to estimate the observed parameters
such as the radio luminosity and intensity of SZ-distortions at the redshifts
of observation. We, further, quantify the effects of various relevant physical
parameters of the radio galaxies, such as the jet power, the time scale over
which the jet is active, the evolutionary time scale for the lobe, etc on the
observed parameters. For current SZ observations towards galaxy clusters, we
find that the non-thermal SZ distortions from radio lobes embedded in galaxy
clusters can be non-negligible compared to the amount of thermal SZ distortion
from the intra-cluster medium and, hence, can not be neglected. We show that
small and young (and preferably residing in a cluster environment) radio
galaxies offer better prospects for the detection of the non-thermal SZ signal
from these sources. We further discuss the limits on different physical
parameters for some sources for which SZ effect has been either detected or
upper limits are available. The evolutionary models enable us to obtain limits,
previously unavailable, on the low energy cut-off of electron spectrum
($p_{min} \sim 1\hbox{--}2$) in order to explain the recent non-thermal SZ
detection. Finally, we discuss how future CMB experiments, which would cover
higher frequency bands ($>$400 GHz), may provide clear signatures for
non-thermal SZ effect.
