Is there an equilibruim in an unsaturated calcium hydroxide solution?
Equilibria in solutions are given as solubility products, $K_{\text{sp}}$. Your reaction is:

$$\ce{Ca(OH)_2 &lt;=&gt; Ca^2+ + 2OH-}$$
for this, $K_{\text{sp}}=5.5\times 10^{-6}$ (from Wikipedia). What this means, is that in a saturated solution, at equilibrium, you will have:
$$K_{\text{sp}}=[\ce{Ca^2+}]  [\ce{OH-}]^2=5.5\times10^{-6}$$

However, for an unsaturated solution, you will have:

$$[\ce{Ca^2+}]  [\ce{OH-}]^2 &lt;K_{\text{sp}}$$

As mentioned the solution does get cloudy for different reasons, namely the formation of $\ce{CaCO3}$ by reaction with $\ce{CO2}$.