The most common and most likely answer to this crossword clue is the 12 letter word EXAGGERATION
I've seen this crossword clue in Financial Times
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More clues leading to the result EXAGGERATION
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 = exaggeration.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 EXAGGERATION mean?
EXAGGERATION noun- The act of heaping or piling up.
- The act of exaggerating; the act of doing or representing in an excessive manner; a going beyond the bounds of truth, reason, or justice; a hyperbolical representation; hyperbole; overstatement.
- A representation of things beyond natural life, in expression, beauty, power, vigor.