[delphi.com.ar]

Gracias al método compare, puedes definir a tu gusto el orden del TListView.
Esto lo extraje de la ayuda de Delphi:

Código Delphi [-]
{The OnColumnClick event handler sets the global 
  variable to indicate the column to sort and calls AlphaSort}

procedure TForm1.ListView1ColumnClick(Sender: TObject; Column: TListColumn);

begin
  ColumnToSort := Column.Index;
  (Sender as TCustomListView).AlphaSort;
end;


{The OnCompare event handler causes the list view to sort on the selected column}

procedure TForm1.ListView1Compare(Sender: TObject; Item1, 
              Item2: TListItem; Data: Integer; var Compare: Integer);
var
  ix: Integer;
begin
  if ColumnToSort = 0 then
    Compare := CompareText(Item1.Caption,Item2.Caption)
  else begin
   ix := ColumnToSort - 1;
   Compare := CompareText(Item1.SubItems[ix],Item2.SubItems[ix]);
  end;

end;

Saludos!