Lime water react with other gases as well such as SO2 etc but the suspension is less milky due to the formation of a white precipitate as well.
Ca(OH)2 + CO2 → CaCO3 + H2O
milky suspension
Ca(OH)2 + SO2 → CaSO3 + H2O
precipitate
Lime water does not form white precipitate with other gases such as NO2.
Ca(OH)2 + NO2 → Ca(NO3)2 + H2O
orange-red