class ListIndexer
        {
            string[] arr;
            public int Length;
            public ListIndexer(int Size)
            {
                arr = new string[Size];
                Length = Size;
            }
            public string this[int index]
            {
                set { arr[index] = value; }
                get { return arr[index]; }
            }
        }
        private void search_Click(object sender, EventArgs e)
        {
            var list = new ListIndexer(Size: lbCollection.Items.Count);
            for (int i = 0; i < list.Length; i++)
            {
                list[i] = lbCollection.Items[i].ToString();
            }
            MessageBox.Show("Элемент под индексом " + (Convert.ToInt32(index.Text)) + " = " + list[Convert.ToInt32(index.Text)].ToString());
        }