  The positive-to-negative transition of spectral lag is an uncommon feature
reported in a small number of GRBs. An application of such a feature has been
made to constrain the critical quantum gravity energy ($E_{\rm QG}$) of the
light photons under the hypothesis that the Lorentz invariance might be
violated. Motivated by previous case studies, this paper systematically
examined the up-to-date Fermi/GBM GRB sample for the lag transition feature to
establish a comprehensive physical limit on the Lorentz Invariance Violation
(LIV). This search resulted in 32 GRBs with redshift available, which exhibit
the lag-transition phenomenon. We first fit each of the lag-E relations of the
32 GRBs with an empirical smoothly broken power law function, and found that
the lag transition occurs typically at about 400 keV. We then implemented the
LIV effect into the fit, which enabled us to constrain the lower limit of the
linear and quadratic values of $E_{\rm QG}$, which are typically distributed at
$1.5\times 10^{14}$ GeV and $8\times 10^{5}$ GeV, respectively.
