I figured it out. The spinning progress indicator is not missing in Lion; it just does not appear for all Automator types. If the Automator workflow is saved as an Application, the spinning gear will appear in the menu bar while the application is executing. If the Automator workflow is saved as a Service, the spinning gear will not appear. I have confirmed all this on two separate macs running Lion 10.7.2.
Unfortunately, once the type is chosen and the workflow is created as that type, it does not appear possible to convert from one type to another, e.g. from a Service to an Application. At least I haven't seen a way to do it. (If someone knows how to do such a conversion, please advise.) Fortunately, it is rather easy to create a new workflow as the desired type while having the other workflow type open in another window.