  The spectral lags of gamma-ray bursts (GRBs) have been viewed as the most
promising probes of the possible violations of Lorentz invariance (LIV).
However, these constraints usually depend on the assumption of the unknown
intrinsic time lag in different energy bands and the use of a single
highest-energy photon. A new approach to test the LIV effects has been proposed
by directly fitting the spectral lag behavior of a GRB with a well-defined
transition from positive lags to negative lags. This method simultaneously
provides a reasonable formulation of the intrinsic time lag and robust lower
limits on the quantum-gravity energy scales ($E_{\rm QG}$). In this work, we
perform a global fitting to the spectral lag data of GRB~190114C by considering
the possible LIV effects based on a Bayesian approach. We then derive limits on
$E_{\rm QG}$ and the coefficients of the Standard Model Extension. The Bayes
factors output in our analysis shows a very strong evidence for the
spectral-lag transition in GRB~190114C. Our constraints on a variety of
isotropic and anisotropic coefficients for LIV are somewhat weaker than
existing bounds, but they can be viewed as comparatively robust and have the
promise to complement existing LIV constraints. The observations of GRBs with
higher-energy emissions and higher temporal resolutions will contribute to a
better formulation of the intrinsic time lag and more rigorous LIV constraints
in the dispersive photon sector.
