The most common and most likely answer to this crossword clue is the 9 letter word INDECENCY
I've seen this crossword clue in The Times
I
N
D
E
C
E
N
C
Y
Buddy explains!

The straight part
We know that "lewd behaviour" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lewd behaviour = indecency.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 INDECENCY mean?
INDECENCY noun- Lack of decency; the property or degree of being indecent
- Something showing lack of decency; something such as a word that is indecent