Some Quantum Gravity models predict a violation of Lorentz invariance. Namely, the velocity of photons in vacuum could depend on their energies. One possibility for Lorentz Invariance Violation (LIV) searches is to look for energy-dependent delays in the arrival time of very high energy (VHE) photons coming from distant sources such as TeV emitting Active Galactic Nuclei (AGN), mainly blazars. Up to now, observations of flaring AGN have only provided upper limits on LIV energy scale since no significant time-delay was found and confirmed.

However, AGN are not perfect sources for such LIV searches because intrinsic temporal effects can be produced by emission processes, similarly to what has been observed with gamma-ray bursts. With the beginning of the Cherenkov Telescope Array (CTA) operations in the coming decade, significant lags should be measured and the question of the origin of these lags will arise. In particular, propagation effects (LIV) will have to be disentangled from source-intrinsic effects. A precise time-dependent modeling of blazar flares becomes necessary to understand the different origins of these time-delays.

In this contribution we report on time-delay studies for blazars in the VHE domain. Using dif- ferent time-dependent emission scenarios of blazar flares, we illustrate their resulting intrinsic spectral lags and provide tools for further analyses of the fine temporal and spectral behavior of such astrophysical sources. Tightly constraining intrinsic effects should then allow to better high- light any extrinsic contribution due to LIV. Conversely, any significant detection of a time-delay should provide new constraints on emission scenarios.