The most common and most likely answer to this crossword clue is the 5 letter word PEGGY
I've seen this crossword clue in Independent
P
E
G
G
Y
Buddy explains!

The straight part
We know that "Lady" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lady = peggy.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 PEGGY mean?
PEGGY noun- Any of several small warblers, the whitethroat, etc.
- The petty officers' mess steward.