First, you naming conventions are horrendous. Don't leave dropdowns with default names. Give them meaningful names.
2nd you have this in the page load,
Lstfacid.Items.Add("1");
Lstfacid.Items.Add("2");
Lstfacid.Items.Add("3");
Lstfacid.Items.Add("4");
Lstfacid.Items.Add("5");
and this in the set data
DataTable dtfacid = new DataTable();
ListBox2.DataSource = dtfacid;
ListBox2.DataTextField = "Facid";
ListBox2.DataValueField = "Facid";
ListBox2.DataBind();
Your dtfacid DataTable is empty, and that is why you are not seeing anything.
Your data is in Lstfacid. Either bind to that or put your data into the dtfacid object.