The most common and most likely answer to this crossword clue is the 11 letter word INCARCERATE
I've seen this crossword clue in Financial Times
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More clues leading to the result INCARCERATE
Buddy explains!

The straight part
We know that "Lock up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lock up = incarcerate.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 INCARCERATE mean?
INCARCERATE verb- To lock away; to imprison, especially for breaking the law.
- To confine; to shut up or enclose; to hem in.