Reliable models of the thermally pulsing asymptotic giant branch (TP-AGB) phase are of critical importance across astrophysics, including our interpretation of the spectral energy distribution of galaxies, cosmic dust production, and enrichment of the interstellar medium. With the aim of improving sets of stellar isochrones that include a detailed description of the TP-AGB phase, we extend our recent calibration of the AGB population in the Small Magellanic Cloud (SMC) to the more metal rich Large Magellanic Cloud (LMC). We model the LMC stellar populations with the TRILEGAL code, using the spatially-resolved star formation history derived from the VISTA survey. We characterize the efficiency of the third dredge-up by matching the star counts and the $K_{rm s}$-band luminosity functions of the AGB stars identified in the LMC. In line with previous findings, we confirm that, compared to the SMC, the third dredge-up in AGB stars of the LMC is somewhat less efficient, as a consequence of the higher metallicity. The predicted range of initial mass of C-rich stars is between $M_{rm i} approx 1.7 - 3~mathrm{M}_{odot}$ at $Z_{rm i} = 0.008$. We show how the inclusion of new opacity data in the carbon star spectra will improve the performance of our models. We discuss the predicted lifetimes, integrated luminosities and mass-loss rate distributions of the calibrated models. The results of our calibration are included in updated stellar isochrones publicly available.
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