A method for producing lime or dolime, which includes a calcination step for the calcination of calcareous or dolomitic material which is brought into contact with the first fumes which are obtained by combustion of fuel with an oxidizing gas, a cooling of calcined lime or dolime with discharge and collection thereof and a release of a gaseous effluent containing CO2. Subsequent processing steps result in the formation of a CaO-based sorbent material with separation between the CaO-based sorbent material and a CO2-concentrated gas stream which is collected. The recycling of said separated CaO-based sorbent material is recycled into a CO2 depletion step resulting in the extraction of a valorizable fraction of the CaCO3—CaO based charge with a compensatory introduction of fresh CaCO3 in the calcination step.