The most common and most likely answer to this crossword clue is the 6 plus 6 letter word MADAME BOVARY
I've seen this crossword clue in The Guardian
M
A
D
A
M
E
B
O
V
A
R
Y
Buddy explains!
The straight part
We know that "Literary lady" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case literary lady = madame bovary.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.