Cryptic crossword clue
Lemon squash in South Eastern street is most splendid 9

The most common and most likely answer to this crossword clue is the 9 letter word SOLEMNEST

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Buddy explains!

The straight part
We know that "most splendid" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most splendid = solemnest.
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.

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