Cement is one of the fundamental building blocks of truly lasting buildings. It is the glue that holds structures together as mortar, or the incredibly strong building blocks of the structure itself, as concrete. Cement comes in two different types: hydraulic and non-hydraulic. Hydraulic cement bonds by a chemical reaction, and will harden regardless of the dryness of the material. Hydraulic cement could even harden underwater! Non-hydraulic cementer is easier to "invent" but must be kept dry to maintain it's strength.
Early cement was made using hydraulic lime(Ca(OH)2) and a pozzolan, such as Pozzolana. Pozzolana is a sandy, fine volcanic ash. that can found in all volcanic regions in Italy. Other pozzolans are the fly ash from coal-fired power plants or rice husk ash from rice paddy field.
Hydraulic lime can be made from limestone, which must be mined. Most cave systems are through limestone bedrock, which would be a good initial source to find limestone. This limestone then must be burned (thermal decomposition) at a temperature of over 800 degrees (See charcoal) which will render the limestone into Calcium oxide (CaO) or quicklime. This is highly caustic material, and adding water will make it more stable and safer to handle.
To produce dry powdered hydrated lime just sufficient water is added for the quicklime lumps to break down to a fine powder. This material would have a 'shelf life' of only a number of weeks, depending on storage conditions. 'Old' hydrated lime would have partially carbonated and become a less effective binder.
To create the cement, mix the hydraulic lime with the pozzolan in a 2:1 ratio. Two parts lime, one part pozzolan.
Mixing this powdered solution with water (two parts cement powder, one part water) will start the chemical reaction and the cement will begin to bond and harden.