Question

why cannot any other gas like nitrogen turn lime water milky?

Answer 1

Lime water is turned milky by carbon dioxide due to formation of calcium carbonate.The reaction is as follows:
$Ca\left(OH{)}_2\right(l)+C{O}_2(g)\to CaC{O}_3(s)+H_{2}O(l)$

Nitrogen doesnot react with lime water and therefore, it doesnot turn milky.