The most common and most likely answer to this crossword clue is the 10 letter word PROTESTANT
I've seen this crossword clue in The Guardian
P
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More clues leading to the result PROTESTANT
Buddy explains!

The straight part
We know that "Lutheran" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lutheran = protestant.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PROTESTANT mean?
PROTESTANT noun- A member of any of several Christian denominations which separated from the Roman Catholic Church based on theological or political differences during the Reformation (or sometimes later).
- (history) A member of the Church of England or Church of Ireland, as distinct from Protestant nonconformists or dissenters
- Of or pertaining to several denominations of Christianity that separated from the Roman Catholic Church based on theological or political differences during the Reformation.
- One who protests; a protester.
- Protesting