stiff lip vs. a stiff lip


Could you tell me what is the expression?

  1. To say something with stiff lip.
  2. To say something with a stiff lip.

Also, does it mean “to say something grudgingly”?

I’ve never heard it that way; it has always been ‘with a stiff upper lip’, which means courageously or stoically.

self-restraint in the expression of emotion (especially fear or grief) (“The British like to keep a stiff upper lip”)

Thank you MM,
Frankly neither have I, but today I happened upon “she said with stiff lip” while reading a book and it kind of puzzled me.

Perhaps grudgingly, then, or upset in some way and trying to hide it.