Solution:
If your Outlook 2007 users are configured to use NTLM authentication but are receiving a log-in prompt -- which they shouldn't -- you need to modify Outlook Anywhere settings for the Autodiscover service.

More specifically, you need to use the Exchange Management Shell and modify a server-side setting for Outlook Anywhere. This should be done on the server that's running the Client Access server role. For the Autodiscover service, you should set the value for the Server attribute for the EXPR OutlookProvider object to $null for the Outlook Anywhere configuration settings. Here's how:

Make sure you have the proper permissions to modify the settings on the Exchange 2007 Server. For example, log on as an account that has the Exchange Organization Administrator role. Start the Exchange Management Shell and run the following command:

Set-OutlookProvider EXPR -Server $null

In order for the changes to take effect, you should either restart Internet Information Services (IIS) or recycle MSExchangeAutodiscoverAppPool on the Exchange Server that's running the Client Access server role.

Restarting IIS is simple but if you decide to recycle MSExchangeAutodiscoverAppPool, you need to go to Application Pools container in the IIS console. Right-click MSExchangeAutodiscoverAppPool and select Recycle. You won't expect any messages confirming your action but the application pool will get recycled. If you have any doubts whether the recycling of the application pool took place, then you can restart IIS instead, which will also accomplish the same thing.