string sqlQuery = "select pk_supplier, supplier_desc from supplier_dim" +
                                    " where source_system = 'BVD' order by supplier_desc";

 // тут возвращается DadaSet с одним DataTable "bvd".  
 //Этот метод работает, я в нём уверен на 100% 
DataSet ds = _db.ExecuteSelectQuery(sqlQuery, "bvd"); 

lboxBvd.DataSource = ds.Tables["bvd"];  // пробовал ds.Table["bvd"].DefaultVew .. не помогает. 

ds.Dispose();
ds = null;

lboxBvd.ValueMember = "pk_supplier";
lboxBvd.DisplayMember = "supplier_desc";

public struct BvdItem
{
	private string _pk;
	private string _name;
	
	public BvdItem(string pk, string name)
	{
		this._pk = pk;
		this._name = name;
	}
	
	public string Pk { get {return _pk;}}
	public string Name { get {return _name;}}
}

string sqlQuery = "select pk_supplier, supplier_desc from supplier_dim where source_system = 'BVD' order by supplier_desc";
ArrayList rs = _db.ExecuteSelectQuery(sqlQuery);

BvdItem[] items = new BvdItem[rs.Count];
int index = 0;
foreach (object[] col in rs) {
	items[index] = new BvdItem(col[0].ToString(), col[1].ToString());
	index++;
}
			
rs = null;
         
lboxBvd.DataSource = items;
lboxBvd.DisplayMember = "Name";
lboxBvd.ValueMember = "Pk";
	      
items = null;