The most common and most likely answer to this crossword clue is the 9 letter word ROMANCERS
I've seen this crossword clue in The Guardian
R
O
M
A
N
C
E
R
S
Buddy explains!
The straight part
We know that "They are not being true/lovers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they are not being true/lovers = romancers.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 ROMANCERS mean?
ROMANCERS noun- One who romances.
- (entertainment industry) A romantic film or television show.