Some Quantum Gravity (QG) theories, aiming at unifying general relativity and quantum mechanics, predict an energy-dependent modified dispersion relation for photons in vacuum leading to a Violation of Lorentz Invariance (LIV). One way to test these theories is to monitor TeV photons time-of-flight emitted by distant, highly energetic and highly variable astrophysical sources such as flaring active galactic nuclei. Only one time-lag detection was reported so far. We have recently shown however that significant intrinsic time-lags should arise from in situ blazar emission processes at TeV energies and should consequently interfere with LIV searches.

In this contribution we will review how intrinsic time delays and LIV-induced propagation effects can simultaneously impact blazars' observed spectral energy distributions and lightcurves. Using a time-dependent approach, we provide predictions on both contributions for various cases in the frame of a standard one zone synchrotron-self-Compton (SSC) model. We will also introduce hints and methods on how to disentangle intrinsic time delays from extrinsic ones in order to highlight LIV effects.