using System;

using System.Linq;

using System.Xml.Linq;

​

public class Program

{

    public static void Main(string[] args)

    {

        const string xml = @"<Items>

   <Item>

      <Id>id 1</Id>

      <Item>item 1</Item>

      <LastModified>2016-01-01</LastModified>

   </Item>

   <Item>

      <Id>id 2</Id>

      <Item>item 2</Item>

      <LastModified>2016-02-02</LastModified>

   </Item>

</Items>";

​

        var doc = XDocument.Parse(xml);

​

        var lastModified = (DateTime) doc.Descendants("Item")

            .Where(x => (string) x.Element("Id") == "id 2")

            .Elements("LastModified")

            .Single();

        Console.WriteLine(lastModified);

    }

}