  Lorentz Invariance Violation (LIV) manifesting itself by energy dependent
modification of standard relativistic dispersion relation has recently
attracted a considerable attention. Ellis et al. previously investigated the
energy dependent time offsets in different energy bands on a sample of gamma
ray bursts and, assuming standard cosmological model, they found a weak
indication for redshift dependence of time delays suggestive of LIV. Going
beyond the $\Lambda$CDM cosmology we extend this analysis considering also four
alternative models of dark energy (quintessence with constant and variable
equation of state, Chaplygin gas and brane-world cosmology). It turns out that
the effect noticed by Ellis et al. is also present in those models and is the
strongest for quintessence with variable equation of state.
