This article compares the distribution of Ks magnitudes of Large Magellanic Cloud (LMC) asymptotic giant branch (AGB) stars obtained from the DENIS and 2MASS data with theoretical distributions. These have been constructed using up-to-date stellar evolution calculations for low and intermediate-mass stars, and in particular for thermally pulsing AGB stars. A fit of the magnitude distribution of both carbon- and oxygen-rich AGB stars allowed us to constrain the metallicity distribution across the LMC and its star formation rate (SFR). The LMC stellar population is found to be on average 5 − 6 Gyr old and is consistent with a mean metallicity corresponding to Z = 0.006. These values may however be affected by systematic errors in the underlying stellar models, and by the limited exploration of the possible SFR histories. Instead our method should be particularly useful for detecting variations in the mean metallicity and SFR across the LMC disk. There are well defined regions where both the metallicity and the mean-age of the underlying stellar population span the whole range of grid parameters. The C/M ratio discussed in paper I is a tracer of the metallicity distribution if the underlying stellar population is older than about a few Gyr. A similar study across the Small Magellanic Cloud is given in paper III of this series.