  Possible violations of Lorentz invariance (LIV) have been investigated for a
long time using the observed spectral lags of gamma-ray bursts (GRBs). However,
these generally have relied on using a single photon in the highest energy
range. Furthermore, the search for LIV lags has been hindered by our ignorance
concerning the intrinsic time lag in different energy bands. GRB 160625B, the
only burst so far with a well-defined transition from $positive$ lags to
$negative$ lags provides a unique opportunity to put new constraints on LIV.
Using multi-photon energy bands we consider the contributions to the observed
spectral lag from both the intrinsic time lag and the lag by LIV effects, and
assuming the intrinsic time lag to have a positive dependence on the photon
energy, we obtain robust limits on LIV by directly fitting the spectral lag
data of GRB 160625B. Here we show that these robust limits on the quantum
gravity energy scales are $E_{\rm QG,1}\geq0.5\times10^{16}$ GeV for the
linear, and $E_{\rm QG,2}\geq1.4\times10^{7}$ GeV for the quadratic LIV
effects, respectively. In addition, we give for the first time a reasonable
formulation of the intrinsic energy-dependent time lag.
