I have a Json response that I receive from an API call. It has several nested levels as show below (this is a snippet):
\"Items\": [
  {
    \"Result\": {
               
        To start off, I'm not familiar with writing LINQ/LAMBDA using this format ["some"]["thing"]. My first step would be to create some classes/objects to house the data in to ease creating any code afterwards.
e.g.
public class Result
{
    public Guid Id { get; set; } 
    public string Name { get; set; },
    public DateTime StartDate  { get; set; }
    //you get the idea
}
But possibly try the following?
    var result = from p in data["Data"]["Items"].Children()
                 where (bool)p["Result"]["ServiceAgreement"]["AdditionalItems"]["ScheduleBased"] == true
                    && (p["Result"]["ServiceAgreement"]["AdditionalItems"]["PayCycle"]).Where(o => o.["ScheduleBased"] == true)
                 select new
                 {
                     Name = (string)p["Result"]["Client"]["Name"],
                     Id = (string)p["Result"]["Client"]["Id"]
                 };
                                                                        You can deserialize the JSON into a dynamic object, and then use Linq to Objects:
    [TestMethod]
    public void TestMethod1()
    {
        const string json = @"""Items"": [
{
""Result"": {
  ""Id"": ""191e24b8-887d-e111-96ec-000c29128cee"",
  ""Name"": ""Name"",
  ""StartDate"": ""2012-04-03T00:00:00+01:00"",
  ""EndDate"": null,
  ""Status"": {
    ""Name"": ""Active"",
    ""Value"": 5
  },
  ""Client"": {
    ""Id"": ""35ea10da-b8d5-4ef8-bf23-c829ae90fe60"",
    ""Name"": ""client Name"",
    ""AdditionalItems"": {}
  },
  ""ServiceAgreement"": {
    ""Id"": ""65216699-a409-44b0-8294-0e995eb05d9d"",
    ""Name"": ""Name"",
    ""AdditionalItems"": {
      ""ScheduleBased"": true,
      ""PayFrequency"": {
        ""Id"": ""981acb72-8291-de11-98fa-005056c00008"",
        ""Name"": ""Weekly"",
        ""AdditionalItems"": {}
      },
      ""PayCycle"": [
        {
          ""Name"": ""Schedule Based"",
          ""ScheduleBased"": true,
          ""SelfBilling"": false,
          ""Id"": ""a8a2ecc4-ff79-46da-a135-743b57808ec3"",
          ""CreatedOn"": ""2011-09-16T23:32:19+01:00"",
          ""CreatedBy"": ""System Administrator"",
          ""ModifiedOn"": ""2011-09-16T23:32:19+01:00"",
          ""ModifiedBy"": ""System Administrator"",
          ""Archived"": false
        }
      ]
    }
  }
}
}
]";
        dynamic data = System.Web.Helpers.Json.Decode("{" + json + "}");
        var result = from i in (IEnumerable<dynamic>)data.Items
                     where i.Result.ServiceAgreement.AdditionalItems.ScheduleBased == true
                     select new
                            {
                                i.Result.Client.Name,
                                i.Result.Client.Id
                            };
        Assert.AreEqual(1, result.Count());
        Assert.AreEqual("client Name", result.First().Name);
        Assert.AreEqual("35ea10da-b8d5-4ef8-bf23-c829ae90fe60", result.First().Id);
    }
Note that I had to add brackets { and } around your example json string, or else the .NET json parser doesn't like it.