It's not that clouds only approach mountain ranges on the lush side. It's that mountains are lush on the side that clouds approach them. Also these clouds only approach the mountains because they are pushed by prevailing winds. It's the pressure of those winds that forces the clouds to climb the mountains. Clouds can't penetrate the soil so they can only rise as the pressure builds up behind them. And as the clouds rise the air becomes less dense and colder. At lower pressure and ower temperature the air loses it's capacity to hod water. That's why it rains on the side of the mountain that the clouds approach. Once this air with its clouds are pushed over the mountain tops it has lost a great deal of water and its ability to hold water grows as it falls down the other side of the mountains, On that side it becomes more difficult to get any rain.
The prevailing winds in North America blow from west to east. That is why the western slopes of the rocky mountains are lush and the American deserts are located to the east of the rockies. The effect is much less pronounced along the east coast because the Appalachians are much smaller than the rockies.
