I will be honest, I'm not that thrilled with this thread on account of the fact that anything I do will feel like "proof-texting". The bottom line is Luther wrote oodles of stuff, there is just so much to use that to ask for specific quotes to prove ourselves "Lutheran" I could honestly make churches of other backgrounds look "Lutheran".
But for the sake of this thread I will pose an example and offer some links:
From his famous tract Freedom of a Christian Luther writes:
"A Christian is the most free Lord of all, subject to none.
A Christian is the most dutiful servant of all, and subject to everyone."
The ELCA embraces the notion of salvation by grace alone through faith alone. It encounters reality with the freeing power of the gospel and structures its worship, theology, and life around this reality. Ultimately, it makes its decisions (the good and the bad) on the basis that we are a broken and diverse people, who have only one hope in life, a gracious and merciful God.
But the ELCA recognizes that we do not live in isolation, rather, we live in a broken world where God's Law and justice are ignored. Thus, it never stops at being saved, but always follows that up with the question "What about your neighbor" for ultimately, that is why we are still here. We are freed so that our lives may be spent for their sake instead of our own. This has caused the ELCA to be very aware of issues in relation to social justice. Where it has turned its attention particularly to the outcast.
This is sort of a general statement, but it seemed that the thread wanted some generalizations.
Here are some relevant links from the ELCA webpage:
This one, while it does not quote Luther, lays out a few foundational Lutheran beliefs and acknowledges the Lutheran Confessions as the true witness to the Gospel.
ELCA Confession of Faith - Evangelical Lutheran Church in America
Below is a site with a link to the new statement on sexuality: gift and trust that is being presented to the churchwide assembly this summer. In relevance to this thread I would recommend reading section II: A Distinctly Lutheran Approach, which will give you an example of using Lutheran theology and quoting Luther which is what you were asking for. Other people might lift up other statements and such (which might even be better to lift up ones that have passed through the assembly) but I had recently read this one and remembered that section.
Recommended Proposed Social Statement - Evangelical Lutheran Church in America
Hope this helps.
Pax