The most common and most likely answer to this crossword clue is the 7 letter word MISSING
I've seen this crossword clue in The Times
M
I
S
S
I
N
G
Buddy explains!
The straight part
We know that "Lost without being lost" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lost without being lost = missing.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 MISSING mean?
MISSING verb- To fail to hit.
- To fail to achieve or attain.
- To avoid; to escape.
- To become aware of the loss or absence of; to feel the want or need of, sometimes with regret.
- To fail to understand; to have a shortcoming of perception; overlook.
- To fail to attend.
- To be late for something (a means of transportation, a deadline, etc.).
- To be wanting; to lack something that should be present.
- (said of a card) To fail to help the hand of a player.
- To fail to score (a goal).
- To go wrong; to err.
- To be absent, deficient, or wanting.
- A value that is missing.
- Not able to be located; gone, misplaced.
- Not present when it (they) should be.
- Of an internal combustion engine: running roughly due to an occasional lack of a spark or other irregular fault.