I've found the answer to my problem: The LongListSelector is not part of the normal libraries. It is part of the Windows Phone Toolkit library, which must be added beforehand with NuGet.
Add to your xaml the new namespace:
xmlns:toolkit="clr-namespace:Microsoft.Phone.Controls;assembly=Microsoft.Phone.Controls.Toolkit"
Now you can access the LongListSelector with
<phone:LongListSelector/>
You can then assign an ItemsSource and can work with it even from blend with design data.