My wife (who has a Geography degree) told me that rain can be generated when moist air is pushed up the side of a mountain. This makes sense from a thermodynamic point of view, but I was wondering what scale we are talking about.

It so happens we live in a mountainous area, and I often see dark clouds over the other side of the mountains. The prevailing wind is always towards us, and when it rains, it looks really bad on the other side, but somewhat ordinary by the time it gets to where we live.

The lake on the far side of the mountain is at around 400 m, the mountain is a somewhat flat ridge peaking at 1100 m, and our side of the lake is at around 700 m.

Is most of the water dumped on the far side from us?

迎风面700 m高差绝对足以触发地形对降水的影响。因此，从你的描述来看，山脉影响你得到的降水似乎很有道理。