Feminine version of "gentleman and a scholar"

Perhaps a "learned lady" would be somewhat equivalent to "a gentleman and a scholar."

In this phrase, learned (lur-nid) is defined as:

1. having great knowledge or erudition
2. involving or characterized by scholarship

And a lady is:

1. A well-mannered and considerate woman with high standards of proper behavior.

I don't think there is an exact equivalent. The problem is that you are asking for a phrase with these incompatible connotations:

• It should be an old-fashioned idiom. (A modern phrase would not have the same ring to it: notice that it's rare to call somebody a "scholar" these days, except in a rather narrow, technical sense.)
• It should suggest that she is scholarly.
• It should suggest that she possesses the qualities admired in a lady.

They are incompatible because, traditionally, female scholarship was not considered ladylike. A female scholar was considered a kind of de-feminised monster.

I can only think of one proper word for an intellectual woman: bluestocking. The etymology is given at Etymonline and Wikipedia, but as you would guess, originally the term was derisive and not appreciative. The situation is different today, for example, Chambers just states:

An intellectual woman

There is another substitute from the French: bas bleu, but the etymological connotations are the same.

This is a rather archaic phrase. The basic idea behind it is that the man in question, rather than being someone who defines himself by labor and/or physical activity (as typical men do), is someone who is genteel, and cares about higher intellectual pursuits. Its kind of the opposite of saying someone is "a man of action".

The problem with applying this to a woman is that unlike with men, this is exactly how a proper lady was supposed to be. Mostly. There weren't supposed to be any "women of action". So in theory there should be no need to say such a thing about a woman.

I'd say that if you are worried about gender equity, this phrase is so loaded down with gender biases that turning it around it hopeless. You should avoid it altogether.