The most common and most likely answer to this crossword clue is the 12 letter word INDIFFERENCE
I've seen this crossword clue in The Times
I
N
D
I
F
F
E
R
E
N
C
E
Buddy explains!

The straight part
We know that "Lack of interest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lack of interest = indifference.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.
Crossword Answer definitions
INDIFFERENCE noun- The state of being indifferent.
- Unbiased impartiality.
- Unemotional apathy.
- A lack of enthusiasm.
- Unconcerned nonchalance.