This will not delete the Data from Database it will just delete the Data from DataTable that you have kept in ViewState.
HTML
<asp:ListView ID="lvCustomers" runat="server" OnItemDeleting="lvCustomersItemDeleting"
    GroupPlaceholderID="groupPlaceHolder1" ItemPlaceholderID="itemPlaceHolder1">
    <LayoutTemplate>
        <table cellpadding="0" cellspacing="0">
            <tr>
                <th>
                    CustomerId
                </th>
                <th>
                    ContactName
                </th>
                <th>
                    Country
                </th>
                <th>
                </th>
            </tr>
            <asp:PlaceHolder runat="server" ID="groupPlaceHolder1"></asp:PlaceHolder>
        </table>
    </LayoutTemplate>
    <GroupTemplate>
        <tr>
            <asp:PlaceHolder runat="server" ID="itemPlaceHolder1"></asp:PlaceHolder>
        </tr>
    </GroupTemplate>
    <ItemTemplate>
        <td>
            <asp:Label ID="lblCustomerId" Text='<%# Eval("CustomerId") %>' runat="server" />
        </td>
        <td>
            <asp:Label ID="lblContactName" Text='<%# Eval("ContactName") %>' runat="server" />
        </td>
        <td>
            <asp:Label ID="lblCountry" Text='<%# Eval("Country") %>' runat="server" />
        </td>
        <td>
            <asp:LinkButton ID="lnkDelete" CommandName="Delete" runat="server" Text="Delete"></asp:LinkButton>
        </td>
    </ItemTemplate>
</asp:ListView>
Namespace
using System.Data;
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.AddRange(new DataColumn[3] { new DataColumn("CustomerId", typeof(int)),
                        new DataColumn("ContactName", typeof(string)),
                        new DataColumn("Country",typeof(string)) });
        dt.Rows.Add(1, "John Hammond", "United States");
        dt.Rows.Add(2, "Mudassar Khan", "India");
        dt.Rows.Add(3, "Suzanne Mathews", "France");
        dt.Rows.Add(4, "Robert Schidner", "Russia");
        ViewState["DataTable"] = dt;
        lvCustomers.DataSource = dt;
        lvCustomers.DataBind();
    }
}
protected void lvCustomersItemDeleting(object sender, ListViewDeleteEventArgs e)
{
    DataTable dt = (DataTable)ViewState["DataTable"];
    dt.Rows.RemoveAt(e.ItemIndex);
    ViewState["DataTable"] = dt;
    lvCustomers.DataSource = dt;
    lvCustomers.DataBind();
}