Lime water reacts with carbon dioxide (CO2) in a two-step process. Limewater is calcium hydroxide dissolved in water.
Ca(OH)2 + H2O → Ca++ 2OH-
Then, the Ca++ reacts with the CO2 to give calcium carbonate which is very insoluble in water:
Ca(OH)2 + CO2 → CaCO3 + H2O
CaCO3 + H2O + CO2 → Ca(HCO3)2