Binding to datacontext parent property - WPF

I have a DataGrid:

 <DataGrid x:Name="DG" ItemsSource="{Binding}" AutoGenerateColumns="False">
     <DataGrid.Columns>
          <DataGridTextColumn Header="?" Binding="{Binding l}">
          </DataGridTextColumn>
     </DataGrid.Columns>
  </DataGrid>

There is a collection of class X in the DataContext DataGrid:

public ObservableCollection<xxx> col{ get; set; }// = DataContext of DG

    private string lName;

    public string LName
    {
        get { return lName; }
        set
        {
            lName= value;
            NotifyPropertyChanged("LName");
        }
    }

I want lName to be the header of a specific column in a DataGrid

I try like this:

 <DataGridTextColumn  Binding="{Binding l}">//l=prop of xxx class that contains the collection
                                <DataGridTextColumn.HeaderTemplate>
                                    <DataTemplate>
                                        <TextBlock Text="{Binding DataContext.LName,
                       RelativeSource={RelativeSource AncestorType=DataGrid}}"/>
                                    </DataTemplate>
                                </DataGridTextColumn.HeaderTemplate>
                            </DataGridTextColumn>

Does not work

how to do it?