With stiff upper lip, there's nothing I demand, squalidly housed (9)

I believe the answer is:

stoically

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'with' is the definition.
Both the answer and definition are adverbs. Perhaps they are linked in a way I don't understand?

I don't understand the rest of the clue.

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(Another definition for stoically that I've seen is " With fortitude".)

I've seen this clue in The Times.

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