Question

<asp:ListView runat="server" ID="lvOuter" DataKeyNames="Id">
    <LayoutTemplate>

    </LayoutTemplate>
    <ItemTemplate>
        <asp:ListView runat="server" ID="lvinner" DataKeyNames="Id" DataSource='<%# Eval("Collection") %>'
            OnItemDataBound="lvGoalsInner_DataBound">
            <LayoutTemplate>
             **Set X from the outer listview**
            </LayoutTemplate>
            <ItemTemplate>
            </ItemTemplate>
        </asp:ListView>
    </ItemTemplate>
</asp:ListView>

Where X is a property of the class whose objects are assigned to the parent data source.

Answer 1

<asp:ListView runat="server" ID="lvinner" DataKeyNames="Id" DataSource='<%# Eval("Collection") %>'
      OnDataBound="lvGoalsInner_DataBound">
  <LayoutTemplate>
    <asp:Literal 
       runat="server" 
       ID="ltTitle" 
       Text='<%# DataBinder.Eval((Container.Parent as ListViewDataItem).DataItem, "Title") %>' />
  </LayoutTemplate>
  <ItemTemplate>
  </ItemTemplate>

protected void lvGoalsInner_DataBound(object sender, EventArgs e)
        {
            (sender as ListView).FindControl("ltTitle").DataBind();
        }

The handler is for DataBound not, ItemDataBound.