Each string has to be converted to an int individually - if your list box contains the values 1, 2, and 3, then your strings will be "1", "2" and "3", which are no integers. They are the string representation of integers instead.
To convert them, you need to convert each element to an integer, using the Parse or TryParse methods.
I would do it this way:
List<int> items = new List<int>();
foreach (string s in listBox1.Items)
foreach (string s in listBox2.Items)
If I needed the data as an array after this, I would convert it:
int array = items.ToArray();