Look at the reaction:
Ca(OH)2 + 2 NH4Cl <--> 2 NH3 (g) + 2 H2O + CaCl2
It is known that the solubility of ammonia decreases when NaCl is added to a solution. So as the Ca(OH)2 dissolves/reacts more ionic CaCl2 is created that decreases the solubility of the NH3 driving the reaction to the right. This implies that NH3 is expelled and Ca(OH)2 is dissolved.
Another way of describing what is happening is the increase in ionic interactions from the "non-common ion effect". As a result, "a sparingly-soluble salt will be more soluble in a solution that contains non-participating ions." See http://www.chem1.com/acad/webtext/solut/solut-6b.html
. This is also referred to as the "Salt Effect" to quote from Wikipedia "
The salt effect refers to the fact that the presence of a salt which has no ion in common with the solute, has an effect on the ionic strength of the solution and hence on activity coefficients, so that the equilibrium constant, expressed as a concentration quotient, changes. (see http://en.wikipedia.org/wiki/Solubility_equilibrium
). For more advanced details see http://www.jim.or.jp/journal/e/pdf3/45/04/1317.pdf
. To quote from the abstract: "We developed a chemical model to analyze ionic equilibria in a cobalt chloride solution at 298K. The chemical model consisted of
chemical equilibria, mass and charge balance equations. The activity coefficients of solutes and water activity were calculated with Bromley
equation. Values of the equilibrium constants for the formation of cobalt chloride complexes at zero ionic strength and of the interaction
parameters were estimated by applying Bromley equation to the reported equilibrium constants at different ionic strength". Now, in the current context, note that NH4Cl/NO3 are salts of a weak base and strong acid, which are highly ionic and have correspondingly low pHs.