Hi Noamon -
Kim has said it exactly. The weather in Switzerland depends heavily on the altitude. For example, the highest alpine road passes are still blocked by snow in late May, and usually do not open until early June. In the lower areas, the flowers are blooming and the fields are green.
I try every year to go to Switzerland in May. I do not go up in the Alps then.
My aim is to visit villages in the countryside, such as the Emmental, or the Three Lakes Region near the French border. Those are at about the same altitude as Luzern, but have slightly different climates due to the way the mountains alter the weather patterns for small regions of the country. In May, there are certainly rainy days, but I count on more sun than rain, and get it.
Switzerland does not have an intense concentrated rainy season, such as the monsoon season in some countries.
If you were to pick one month that lets you see the best of all parts of Switzerland, it is usually September. October can be quite nice as well. August is full of tourists.
There tends to be more rain in the Spring months...April,May, June. However, I had to go for 10 days in mid-April 2014, since I could not go in May, and had 9 days of perfect weather, and one day when I took a train to another region to get the good weather there.
The attached image was taken near Sumiswald in the Emmental in mid-April 2014. The Alps in the background are still covered with snow, and the grass in the fields has mostly not become really green yet. Some fields are plowed and planted. That was unusually good weather for April. In May, it would not be surprising, and the Alps would still show a lot of snow.
We almost always go in September as well as May. One out of the 12 Septembers that we have gone had two weeks straight of clouds and rain. The others were quite dry, sunny, and had moderate temperatures.
That's my experience.