The most common and most likely answer to this crossword clue is the 8 letter word BURGLARY
I've seen this crossword clue in The Daily Telegraph
B
U
R
G
L
A
R
Y
More clues leading to the result BURGLARY
Buddy explains!

The straight part
We know that "Domestic lifting?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case domestic lifting? = burglary.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 BURGLARY mean?
BURGLARY noun- The crime of unlawfully breaking into a vehicle, house, store, or other enclosure with the intent to steal.