  This paper investigates a signature of Lorentz invariance violation with the
$t\bar{t}$ production at the LHC and future hadron colliders. Possible
deviations from the Lorentz symmetry remain poorly constrained in the top quark
sector. With a dedicated analysis of $t\bar{t}$ events produced at the LHC,
bounds in the top sector can be improved by up to three orders of magnitude
relative to Tevatron, the only measurement existing so far. The sensitivity
will be even further enhanced at the HL-LHC and future colliders.
