This is a good questions and one that I hope some of the other cadre of characters can chime in on here. My gut on this one is that we will all pin-point different aspects of our tradition to emphasize as important.
If I could start with one recommendation for anyone out there thinking about Lutheranism, I would highly recommend reading Luther himself. For one thing, Luther is the de facto founder of all Protestantism. Thus, a reading of the primary sources might actually find much more similarities in thought than previously thought, as well as raise important questions for people thinking through their own traditions. LCMS Lutheranism is a building from the texts of Scripture and Luther and as any search on American Lutheranism will discover, there are all sorts of Lutheran denominations that bring Scripture an Luther together. I happen to think that the LCMS does the best job, even with all its wrinkles and not simply for payroll reasons 
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With reading Luther in mind, I think three things are really keen to understanding Christ and culture issues generally and science and religion issues specifically.
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Epistemological Ordering:
The first is that epistemological ordering that has been mentioned in this thread as well as the divine action thread. Lutherans have always been cautious with beginning times and end times. This is due to the fact that our epistemological method of knowing things Scripturally are always filtered through Calvary. It means, and this will sound rather weird to Christian ears including Lutheran, that Genesis is really not something that matters much as one is coming to faith! But hold on, let me explain myself a bit. Because the veracity of Scripture is secured by Jesus’ death and resurrection, and He speaks highly of Genesis 1-3, then I trust that Genesis is true and the rest of Scripture in its Christocentricity. I don’t need to make sure everything fits well with current science or not as the eternal Word of God will outlast any contingent scientific theory. It does mean, however, that we must tend carefully to the historical evidence for the resurrection, however, which is why I do not consider myself a fideist. I don’t start with the Bible being true, but discover it through Christ and back-up that revelation through the fact that it looks like it really happened in human history that God was in Christ reconciling the world to himself. I do believe that what scientists such as Swamidass are doing is very important, but will always get trumped by discussions of the resurrection. I think he would agree with me on this though. And if he doesn’t, he can always find a little comfort in that the philosopher is more often than not even further removed from the center of these conversations as our laboratories are the mind which are deeper and darker than any study of nature reveals
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Freedom and Courage to Imagine:
If Calvin was the god intoxicated theologian, Luther was the Christ intoxicated theologian. I suppose this makes sense as Jesus did turn water to wine… Anyway, due to the fact that Lutherans are so intoxicated by the forgiveness offered in Christ, we are free to serve our neighbors in radical ways. This is the insight of Luther’s “Freedom of a Christian” tract with the famous paradoxical statement,
A Christian is an utterly free man, lord of all, subject to none.
A Christian is an utterly dutiful man, servant of all, subject to all.
Out of this paradox to be free and serve, comes a unique sense of Lutheran vocation that may be helpful for larger Christendom. The idea is that God places us in contexts that require service. A young student may get intrigued by biology as a grade school student, then learns about evolutionary theory in high school, is committed to becoming a biologist but is constantly bothered by the fact that whenever discussion turn toward science at church, evolutionary biology is demonized. This is problematic because the church actually needs that student to be a biologist, even an evolutionary biologist. Who better to serve that community than that student as he/she becomes inducted into the guild of biology or philosophy or history or whatever… Yet, we get hung-up on the dangers of evolution, the scriptural problems, the materialistic implications. We do not have the courage nor the imagination to encourage our young to travel into the “lion’s den” of science, trusting that the Lord will preserve them.
I would like to submit to the larger American Christian scene that the epistemological ordering discussed in (1) and the paradoxical notion of freedom to serve (2), while specifically Lutheran, might better structure a Christian response and engagement with science.
- Freedom to Fail (Continual Need for Forgiveness)
Bound up with my point (1) and my point (2) is the fact that failure is inevitable. The freedom and courage to imagine might entail crucifixion symbolically and in the historical cases literally! We cannot and avoid and will continually invite suffering into our lives as we live out our vocations. However, this again is the great insight of Lutheran theology, that everything that takes place in the world, under the Law, should drive us back to Christ. The “soldiers” that are sent into the world to freely and courageously serve their neighbors will constantly be rejected, harmed, abused, and need to be reminded constantly of their identity grafted into Jesus death and resurrection. The free forgiveness of sins, personally and existentially applied to the individual through the words “for you” carry more power than I think most of us Christians realize. Lutherans may get criticized for keeping things too simple by not wanting to stray too far from Christ’s death and resurrection, relentlessly iterating the same message over and over again. However, in that message of forgiveness is power, the power to move mountains. This is were I think the pastors are absolutely crucial to the relationship between science and theology, not so much as soldiers on the front line, but the medics that continually drag our broken bodies back to the cross. No more anti-evolution, anti-politcs, anti whatever screeds from the pulpit (plenty of Lutherans are guilty of this as well), I need to hear from the great physician daily and weekly that “it is finished” and that I am set free AGAIN to go and serve my neighbor with courage and imagination.
I’m not sure how helpful or different that is from other traditions, and, of course, these are forum thoughts not given the more scholarly attention they deserve from me. I should note as well that I am reading through some material from @CPArand that is relevant to this conversation and perhaps as it get published on the Concordia Seminary blog might be of interest for those looking at Lutheran distinctives. In the meantime, I’d be curious as to thoughts from Lutherans and non-Lutherans?