Hi counterkin,

You need to pass as query string to the Handler.

Refer below modified code.

HTML

<asp:FileUpload ID="postedFile" runat="server" />
<asp:Button ID="btnUpload" runat="server" Text="Upload" />
<asp:Label ID="lbl_ID" runat="server" Text="50018"></asp:Label>
<div class="progress" style="display: none">
    <div class="progress-bar" role="progressbar"></div>
</div>
<div id="lblMessage" style="color: Green"></div>

<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/3.7.1/jquery.min.js"></script>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" />
<script type="text/javascript">
    $("body").on("click", "[id*=btnUpload]", function () {
        $.ajax({
            url: 'Handler.ashx?Id=' + $("[id*=lbl_ID]").html(),
            type: 'POST',
            data: new FormData($('form')[0]),
            cache: false,
            contentType: false,
            processData: false,
            success: function (file) {
                setTimeout(function () {
                    $(".progress").hide();
                    $("#lblMessage").html("<b>" + file.name + "</b> has been uploaded.");
                }, 1000);
            },
            error: function (a) {
                $("#lblMessage").html(a.responseText);
            },
            failure: function (a) {
                $("#lblMessage").html(a.responseText);
            },
            xhr: function () {
                var fileXhr = $.ajaxSettings.xhr();
                if (fileXhr.upload) {
                    $(".progress").show();
                    fileXhr.upload.addEventListener("progress", function (e) {
                        if (e.lengthComputable) {
                            var percentage = Math.ceil(((e.loaded / e.total) * 100));
                            $('.progress-bar').text(percentage + '%');
                            $('.progress-bar').width(percentage + '%');
                            if (percentage == 100) {
                                $('.progress-bar').text('100%');
                            }
                        }
                    }, false);
                }
                return fileXhr;
            }
        });
    });
</script>

Handler

C#

<%@ WebHandler Language="C#" Class="Handler" %>

using System;
using System.IO;
using System.Net;
using System.Web;
using System.Web.Script.Serialization;

public class Handler : IHttpHandler
{
    public void ProcessRequest(HttpContext context)
    {
        //Check if Request is to Upload the File.
        if (context.Request.Files.Count > 0)
        {
            //Fetch the Label value.
            string id = context.Request.QueryString["Id"];

            //Fetch the Uploaded File.
            HttpPostedFile postedFile = context.Request.Files[0];

            //Set the Folder Path.
            string folderPath = context.Server.MapPath("~/Uploads/");

            //Set the File Name.
            string fileName = Path.GetFileName(postedFile.FileName);

            //Save the File in Folder.
            postedFile.SaveAs(folderPath + fileName);

            //Send File details in a JSON Response.
            string json = new JavaScriptSerializer().Serialize(
                new
                {
                    name = fileName
                });
            context.Response.StatusCode = (int)HttpStatusCode.OK;
            context.Response.ContentType = "text/json";
            context.Response.Write(json);
            context.Response.End();
        }
    }

    public bool IsReusable
    {
        get
        {
            return false;
        }
    }
}

VB.Net

<%@ WebHandler Language="VB" Class="Handler" %>

Imports System
Imports System.IO
Imports System.Net
Imports System.Web
Imports System.Web.Script.Serialization

Public Class Handler : Implements IHttpHandler
    Public Sub ProcessRequest(ByVal context As HttpContext) Implements IHttpHandler.ProcessRequest
        'Check if Request is to Upload the File.
        If context.Request.Files.Count > 0 Then
            'Fetch the Label value.
            Dim id As String = context.Request.QueryString("Id")

            'Fetch the Uploaded File.
            Dim postedFile As HttpPostedFile = context.Request.Files(0)

            'Set the Folder Path.
            Dim folderPath As String = context.Server.MapPath("~/Uploads/")

            'Set the File Name.
            Dim fileName As String = Path.GetFileName(postedFile.FileName)

            'Save the File in Folder.
            postedFile.SaveAs(folderPath + fileName)

            'Send File details in a JSON Response.
            Dim json As String = New JavaScriptSerializer().Serialize(New With {
                .name = fileName
            })
            context.Response.StatusCode = CInt(HttpStatusCode.OK)
            context.Response.ContentType = "text/json"
            context.Response.Write(json)
            context.Response.End()
        End If
    End Sub

    Public ReadOnly Property IsReusable() As Boolean Implements IHttpHandler.IsReusable
        Get
            Return False
        End Get
    End Property
End Class

Screenshot