<asp:DataList ID="DataList1" runat="server"
                     oneditcommand="DataList1_EditCommand" >
                
            <ItemTemplate>
                    <asp:Label ID="lblAddressID" runat="server" Text='<%# Bind("addressID") %>'/>
                    <asp:Label ID="lbl" runat="server" />
                    <asp:Button runat="Server" ID="cmdEdit" CommandName="Edit" Text="Edit"/>
            </ItemTemplate>
            
            <EditItemTemplate>  
                    <asp:TextBox ID="txtAddressID" runat="server" Text='<%# Bind("addressID") %>' BackColor="#FFFF66" />        
                    <asp:Label ID="lbl" runat="server"/>
                    <asp:Button runat="Server" ID="cmdUpdate" CommandName="Update" Text="Update" />
                    <asp:Button runat="Server" ID="cmdCancel" CommandName="Cancel" Text="Cancel"/>
            </EditItemTemplate>
       </asp:DataList>

private void BindDataList()
    {
        int userId = Convert.ToInt32(ProfileInfo.GetUserID());

        DataList1.DataSource = CatalogAccess.GetAddressByUserID(userId);
        DataList1.DataBind();

        foreach (DataListItem item in DataList1.Items)
        {

            Label lbl = (Label)item.FindControl("lbl");
            lbl.Text = "myLabel";

        }
    }


    protected void DataList1_EditCommand(object source, DataListCommandEventArgs e)
    {
        int userId = Convert.ToInt32(ProfileInfo.GetUserID());
        
        DataList1.EditItemIndex = e.Item.ItemIndex;
        DataList1.DataSource = CatalogAccess.GetAddressByUserID(userId);
        DataList1.DataBind();

        Label lbl = (Label)e.Item.FindControl("lbl") as Label;
        lbl.Text = "edit mode";
    }

Try to access it at ItemDataBound event of DataList:

protected void DataList1_ItemDataBound(object sender, DataListItemEventArgs e)
{
	if (e.Item.ItemType == ListItemType.EditItem)
	{
		Label lb = (Label)e.Item.FindControl("lb");
                if(lb != null)
                {
                    lb.Text = "Hello";
                }
	}
}

do this change:

protected void DataList1_EditCommand(object source, DataListCommandEventArgs e)
    {
        int userId = Convert.ToInt32(ProfileInfo.GetUserID());
        
        DataList1.EditItemIndex = e.Item.ItemIndex;
        DataList1.DataSource = CatalogAccess.GetAddressByUserID(userId);
        DataList1.DataBind();

        Label lbl = (Label)e.Item.FindControl("lbl") as Label;
        if (lbl != null)
        {
           Label lbl = (Label)DataList1.Items[e.Item.ItemIndex].FindControl("lbl");
           lbl.Text = "edit mode";
        }
    }