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tokens: spacetime (Mattingly 2005 ; Amelino-Camelia 2013 ). Any possible violation of Lorentz invariance would have far-reaching consequences for our understanding of the nature, i.e., the pillars of modern physics will be shocked and new physics is needed (Cao et al. 2018a ). Therefore, the pursuit of testing the possible LIV at much higher precision has continued in recent decades, concerning various astrophysical and cosmological observations. Formulating and quantitatively interpreting the test of LIV is another question: an interesting proposal, in this respect, has been formulated in the frameworks of many QG: at small spatial scales, a foamy structure of spacetime predicted by QG theory will interact only with the high-energy photons (Amelino-Camelia et al. 1998 ; Amelino-Camelia Piran 2001 ). In this case, the speed of light is varying at a different energy range in vacuum, i.e., the high and low-energy photons will not reach us at the same time. More specifically, the deformed velocity of light usually takes the form , where E QG is effective QG energy scale, s ± , is a dimensionless parameter depending on the particular QG model, and c is the limiting speed of light on low-energy scales, respectively. On low-energy scales, E ≪ E QG , the effect of LIV will be more obvious and the high-energy photons propagate slower than low-energy photons. Although the QG effect is expected to be very weak (since E QG is typically close to the Planck energy scale), some effects of LIV are expected to increase with energy and over very long distances due to cumulative processes in photon propagation. Therefore, astrophysical searches provide sensitive probes of LIV and its potential signatures, such as the energy-dependent time delay and many other phenomena. Gamma-ray bursts (GRBs), the most luminous astrophysical events observable proposed as distance indicators at high redshift (Pan et al. 2013 ; Cao Zhu 2014 ), create such an opportunity to test the LIV, through the precise measurement of unprecedented very-high-energy photons. Compared with commonly used supernova Ia, the advantages of GRBs lies in their high-energy photons in the gamma-ray band (from KeV to GeV), short spectral lags, and the propagation distance at cosmological scales. Such a natural laboratory provides a possibility of testing LIV, through the well-measured time delays between light curves in different energy bands caused by the LIV. Recently, some advances have been made concerning the limits on LIV using different samples of GRBs (Ellis et al. 2003 , 2006 ; Rodriguez Martínez Piran 2006 ; Jacob Piran 2007 ; Pan et al. 2015 ; Zhang Ma 2015 ; Wei et al. 2017 ; Zhang et al. 2018b ; Zou et al. 2018 ). The original idea of such studies of possible LIV constraints can be traced back to the papers of Ellis et al. ( 2003 ), which developed a method to analyze samples of GRBs with different redshifts and energy bands, by extracting time-dependent features from the GRB signals. It is worth