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