Lime is made from limestone or chalk, which are sedimentary rocks.
Limestone makes up about 10% of the total volume of all sedimentary rocks. Limestone has a biochemical origin (the accumulation of skeletal fragments of marine organisms such as coral, urchin or alga), and a chemical origin (the chemical precipitation of calcium carbonate, as with stalactites and stalagmites).
Limestone is mostly composed of calcite (or calcium carbonate, CaCO3). When composed of calcite and magnesium carbonate (MgCO3), we are talking of dolomite (or calcium magnesium carbonate, Ca,Mg(CO3).