The most common and most likely answer to this crossword clue is the 11 plus 4 letter word ALTERNATIVE FACT
I've seen this crossword clue in Financial Times
A
L
T
E
R
N
A
T
I
V
E
F
A
C
T
More clues leading to the result ALTERNATIVE FACT
Buddy explains!
The straight part
We know that "That’s a lie" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s a lie = alternative fact.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.