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Lois: So in aII those nights together...
...somewhere between brushing teeth
and spooning in the sheets... you didn't think to mention
that you prowI the streets with green Ieather
and a compound bow?

Oliver: WeII, I don't usuaIIy bring
the compound bow.
Meanig he doesn't show up on a date with his bow?
(Oliver is the iconic hero Green Arrow.)

Lois: Oh. So now he's a funny hero.
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She is saying that he keeps his superhero identity secret from the woman he lives with.

That is obviously an important thing to keep secret. It's a BIG secret.

He picks one tiny part of what she said and says that part isn't true. He doesn't deny that he's a superhero, etc. It's deliberately understating that he keeps this important part of his life a secret by quibbling over such a tiny detail. (You may want to look up quibble.)
Comments  
I think he is saying that he usually doesn't bring the bow along while he is prowling the streets. He doesn't mention if he brings them to dates or not.

~Miss Mandy
Students: Are you brave enough to let our tutors analyse your pronunciation?
 BarbaraPA's reply was promoted to an answer.
Thanks!