Is there such a thing as Orthodox Lutheran Christian? I was talking with my buddy the other day. He said he is Orthodox Lutheran Christian. Is that a real thing? I don't think so.
There are several ways in which he could be meaning this.

One, there are indeed churches that identify themselves as Orthodox (big-O) Lutheran. For example: Lutheran Orthodox Church and Orthodox Lutheran Confessional Conference. This would mean he is a member of a specific church/sect that calls themselves these words.

Two, there is a historical era of Lutheranism known as Lutheran orthodoxy, which is mostly historical but has had some resurgence lately.  See: Lutheran orthodoxy. This would mean he probably is theologically educated and can go on at length about the Book of Concord.  This may align closely with #1 above (for example, the OLCC strongly adheres to the Book of Concord).

Three, he may mean an orthodox (practicing, mainline belief) Lutheran. He may mean this as opposed to "those people who call themselves Lutherans but don't go to church or know the first thing about its theology", or he may be referring to some denominational beef - I'd actually put 20 bucks on his meaning is "I'm Missouri Synod and not one of those fruity ELA or ELCA folks," or potentially "I'm ELA instead of one of those fruity ELCA folks."  Those are the three major Lutheran denominations, in decreasing order of cultural conservatism, and like to talk smack about each other in a semi-friendly way.

If you're really curious, ask him "what do you mean exactly by Orthodox?"  In any of these three cases he'll probably be thrilled to hold forth on it for you.