I’ve not been able to parse the distinction between Lutheran and Evangelical
"What is an 'evangelical'?" is complicated. The answer depends on place and time. Once upon a time it was synonymous with "protestant". Lutherans in particular, of all stripes, seem to like the term.
Some argue that the term isn't very useful at this time.
Evangelical doesn’t mean anything anymore when you have John MacArthur, R.C. Sproul, Rick Warren and Joel Osteen all calling themselves evangelicals.