The most common and most likely answer to this crossword clue is the 7 letter word JOUSTED
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result JOUSTED
Buddy explains!

The straight part
We know that "fought for a lady’s favour" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fought for a lady’s favour = jousted.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 JOUSTED mean?
JOUSTED verb- To engage in mock combat on horseback, as two knights in the lists; to tilt.
- To engage in verbal sparring over an important issue. (used of two people, both of whom participate more or less equally)
- To touch penises while engaging in a sex act, especially oral sex.