  The Hubble tension in cosmology is not showing signs of alleviation and thus,
it is important to look for alternative approaches to it. One such example
would be the eventual detection of a time delay between simultaneously emitted
high-energy and low-energy photons in gamma-ray bursts (GRB). This would signal
a possible Lorentz Invariance Violation (LIV) and in the case of non-zero
quantum gravity time delay, it can be used to study cosmology as well. In this
work, we use various astrophysical datasets (BAO, Pantheon Plus and the CMB
distance priors), combined with two GRB time delay datasets with their
respective models for the {\em {intrinsic time delay}}. Since the intrinsic
time delay is considered the largest source of uncertainty in such studies,
finding a better model is important. Our results yield as quantum gravity
energy bound $E_{QG}\ge 10^{17}$ GeV and $E_{QG}\ge 10^{18}$ GeV respectively.
The difference between standard approximation (constant intrinsic lag) and the
extended (non-constant) approximations is minimal in most cases we coincide.
However, the biggest effect on the results comes from the prior on the
parameter $\frac{c}{H_0 r_d}$, emphasizing once again that at current
precision, cosmological datasets are the dominant factor in determining the
cosmology. We estimate the energies at which cosmology gets significantly
affected by the time delay dataset
