This paper presents combinations of inclusive and differential measurements of the charge asymmetry (A(C)) in top quark pair (t(t)over-bar) events with a lepton+jets signature by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. The data correspond to integrated luminosities of about 5 and 20 fb(-1) for each experiment, respectively. The resulting combined LHC measurements of the inclusive charge asymmetry are A(C)(LHC7) = 0.005 +/- 0.007 (stat) +/- 0.006 (syst) at 7 TeV and A(C)(LHC8) = 0.0055 +/- 0.0023 (stat) +/- 0.0025 (syst) at 8 TeV. These values, as well as the combination of A(C) measurements as a function of the invariant mass of the t(t)over-bar system at 8 TeV, are consistent with the respective standard model predictions.