The most common and most likely answer to this crossword clue is the 6 letter word LABRUM
L
A
B
R
U
M
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The straight part
We know that "lip" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lip = labrum.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 LABRUM mean?
LABRUM noun- The uppermost of the mouthparts (trophi) of a typical insect, such as a cockroach. Typically resembles an upper lip and forms part of the roof of the mouth in such insects.
- Any of several lip-like projections.
- A large basin of warm water, with an overhanging lip, in a Roman bath.