The most common and most likely answer to this crossword clue is the 7 letter word GODLESS
I've seen this crossword clue in The Guardian
G
O
D
L
E
S
S
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 = godless.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 GODLESS mean?
GODLESS adjective- Not acknowledging any deity or god; without belief in any deity or god.
- Evil, wicked, worldly.