The most common and most likely answer to this crossword clue is the 9 letter word ATHEISTIC
I've seen this crossword clue in Financial Times
A
T
H
E
I
S
T
I
C
More clues leading to the result ATHEISTIC
- The fellow is entertained by Greek following rationalist philosophy?
- Not believing he’s interrupting classic speech
- Sceptical ambassador is cornered by Greek
- In Greek, man is lacking belief
- Not believing it’s the CIA complex
- Lacking faith, he lives in top floor
- Ungodly fellow is in garret
- Articles – two written about holy man caught doubting God’s existence
- The chap is collared by old Greek against religion
- . Not the praying kind, that man is locked up in loft
Buddy explains!

The straight part
We know that "Lacking faith" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lacking faith = atheistic.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 ATHEISTIC mean?
ATHEISTIC adjective- Of or relating to atheists or atheism