The first example, "A George Lucas Film," isn't possessive like your second example is. It's using George Lucas's name like an adjective. So your two scenarios aren't the same.
In English, you would seldom to never say, "a John's brother." You might say, "a john's brother," which would be the brother of someone who frequented prostitutes. I suppose you could say, "a John's brother," if you meant the brother of some indefinite person named John. For example, "I don't know who he was. He said that he was a John's brother. Do you know someone named John? If so, he was his brother." However, even in that scenario, you would likely hear more people say, "of a John," rather than, "a John's." For example, "He said that he was the brother of a John, or was it a Sam? I can't remember. Do you know a John or a Sam?"