Do we really need a Load Balancer between Workflow Manager Farm and SharePoint ?

Well , It  depends .

If you have a Workflow Manager farm (more than one server) and one of the WFM EndPoints recieve a request without any load balancer ,it balances the load across the WFM servers .Yes thats correct . WFM farm have an internal load balancing mechanizm to do that.

WFMwithoutNLB

But if you don’t use a load balancer ,WFM only balance the load , not switch between endpoints if active endpoint dies . There is only one endpoint be active at a time . And if something happens on that EndPoint or its host machine then you may face an outage even your other servers are alive. Because SharePoint knows only one endpoint url and it is not reachable.
WFMwithNLB

So it depends that how much you want a high availability . Actually in real , load balancer is resposible not to share load , just keeps high availability if an endpoint dies  between your SharePoint farm and WFM farm .

Microsoft.Workflow.Client.AuthenticationException “Authentication Failed”

When attempting to publish a workflow in SharePoint 2013 . you may facing following problem.

System.InvalidOperationException: Operation failed with error Microsoft.Workflow.Client.AuthenticationException: Authentication Failed. Valid credentials must be provided for one of the following protocols: Bearer, Negotiate. HTTP headers received from the server – ActivityId: 440bd264-3528-4880-91c9-03247a2e5e10. NodeId: WFSERVER01. Scope: /SharePoint/default/e72269ca-0e8c-4bd6-800a-9499da19f233. WWW-Authenticate: Bearer realm=”22a5da47-566b-4e0b-90f9-76752903b68e”, client_id=”00000005-0000-000

TroubleShooting Steps
1) First you have to check installation and upgrades:
It is important that any Cumulative Updates (CU) for SharePoint Server 2013 and Workflow Manager are installed in a coordinated fashion. After an update has been performed, several Windows PowerShell cmdlets must be run in order to maintain the connection between the SharePoint Server 2013 farm and the Workflow Manager farm.
Check that you have Service Bus 1.1
Check that you have Workflow Manager 1.0 Refresh installed
Check that you have Workflow Manager 1.0 Refresh Client (must installed all SharePoint Servers)
Check that you have at least SharePoint 2013 SP1.
(Article Date: 24/12/2014)

If you want to use Workflows with Microsoft supportability you need to have latest bits is running.

2) Check Network connections. (Dont miss this step is very important , Even Some Scenarios it looks working while you can save workflows and Worflow Manager Service looks connected but this issue can happen)
SharePoint Servers (WFEs) must able to reach Workflow Manager web site
And also it is a requirement that from Worflow Manager Machine (if it is a different machine) must able to browse the site url which you use to register-spworkflowservice.
Ping both machines that have ip communication
And also Check Proxies

3) Check all host file entries on every server that is there something preventing network communication .

4) Check Firewall rules and communications.

5) Test your credentials are correct or not .

7) Check Workflow Services are running , Workflow Manager Web Site is up and Application pool is alive.

8) If workflow manager is hosted on a different machine check IIS configuration that you have Windows Authentication is enabled.

9) Try re-register workflow service by scopename;
Register-SPWorkflowService -SPSite ‘http://mywebsite’ -WorkflowHostUri ‘https://workflowhost’ -AllowOAuthHttp -scopename “SharePoint”  -Force

10) If it doesnt work ; unregister the Workflow manager from the sharepoint farm
Get-SPWorkflowServiceApplicationProxy | Remove-SPServiceApplicationProxy
and run
Register-SPWorkflowService -SPSite ‘http://mywebsite’ -WorkflowHostUri ‘https://workflowhost’ -AllowOAuthHttp -scopename “SharePoint”  -Force
this will recreate the SPWorkflowServiceApplication Proxy.

(Dont Forget make an iisreset after use “Register-SPWorkflowService”)

11) Verify you have using latest activities are updated through the Workflow Manager.

$credential = [System.Net.CredentialCache]::DefaultNetworkCredentials
$site = Get-SPSite(<siteUri>)
$proxy = Get-SPWorkflowServiceApplicationProxy
$svcAddress = $proxy.GetWorkflowServiceAddress($site)
Copy-SPActivitiesToWorkflowService -WorkflowServiceAddress $svcAddress -Credential $credential -Force $true

Make your test with creating a new workflow and publish.