The most common and most likely answer to this crossword clue is the 9 letter word FAIRYTALE
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More clues leading to the result FAIRYTALE
Buddy explains!

The straight part
We know that "a lie" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a lie = fairytale.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 FAIRYTALE mean?
FAIRYTALE noun- A folktale featuring fairies or similar fantasy characters.
- A story presented as true that is not believable.
- Of the nature of a fairy tale; as if from a fairy tale.