  In this contribution we describe a recent study focused on the lattice
calculation of inclusive decay rates of heavy mesons. We show how the inclusive
calculation can be achieved starting from four-point lattice correlation
functions normalised appropriately. The correlators used in this project come
from gauge ensembles provided by the JLQCD and ETM collaborations. An essential
point of this method is the extraction of spectral densities from lattice
correlators which is obtained using two of the most recent approaches in the
literature. Our results are in remarkable agreement with analytical predictions
from the operator-product expansion. This study represents the first step
towards a full lattice QCD study of heavy mesons inclusive semileptonic decays.
