The results obtained at the LHC for constraining the trilinear Higgs self-coupling of the detected Higgs boson at about 125 GeV, λhhh, via the Higgs pair production process have significantly improved during the last years. We investigate the impact of potentially large higher-order corrections and interference effects on the comparison between the experimental results and the theoretical predictions for the pair production of the 125 GeV Higgs boson at the LHC. We use the theoretical framework of the Two Higgs Doublet Model (2HDM), containing besides the SM-like CP-even Higgs boson h a second CP-even Higgs boson H, which we assume to be heavier, mH>mh. We analyze in particular the invariant mass distribution of the two produced Higgs bosons and show that the loop corrections to the trilinear Higgs couplings λhhh and λhhH as well as interference contributions give rise to important effects both for the differential and the total cross section. We point out the implications for the experimental limits that can be obtained in the 2HDM for the case of the resonant production of the heavy Higgs boson H. We emphasize the importance of the inclusion of interference effects between resonant and non-resonant contributions in the experimental analysis for a reliable determination of exclusion bounds for a heavy resonance of an extended Higgs sector.