It's very near to cheek in two ways (3)

I believe the answer is:

lip

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'cheek in two ways' is the definition.
'lip' can be an answer for 'cheek' (both can mean insolence or rudeness). I am not sure about the 'in two ways' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for lip that I've seen before include "Edge of mouth" , "Rim; impertinence" , "Rim; impudence (slang)" , "Edge; impudent talk" , "Aural impudence" .)

I've seen this clue in The Globe and Mail.

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