According to Kennington, "idea" is used in a precise sense throughout NRH. See for instance, Benardete discussing Kennington here.
Seth: . . . I had told him about the indeterminate dyad. Then he wrote the review of Natural Right and History in which he discovered that it has that structure. That was extraordinary.
Ronna: How did Kennington show that?
Seth: In various ways, like noting how Strauss used "idea" in a very curious manner. There are these refined distinctions between the Plato section [chapter III] and the Aristotle section [chapter IV] about natural right. He discussed the way terms are used in the wrong chapter: it's always in the subsequent chapter [paired chapter] that the idea of something comes up, as opposed to the chapter where it seems relevant.
Here are the appearances of different "ideas" throughout NRH, plus the length in paragraphs of each chapter:
Intro (9 paragraphs)
pg. 1 idea of natural right
Chap I: Natural Right and the Historical Approach (34 paragraphs)
10 idea of natural right
11 idea of philosophy
12 idea of philosophy
30 idea of philosophy
31 idea of natural right
Chap II: Natural Right and the Distinction between Facts and Values (42 paragraphs)
38 idea of science/idea of empirical science
74 idea of science
75 idea of science
80 idea of natural right
Chap III: Origin of the Idea of Natural Right (48 paragraphs)
82 idea of nature
93 idea of natural right
96 "idea of the state"
Chap IV: Classical Natural Right (40 paragraphs)
124 idea of justice
145 idea of man/idea of justice
Chap V: Modern Natural Right
(1 intro paragraph)
V. A: Hobbes (40 paragraphs)
168 idea of political philosophy
180 idea of natural law/idea of man's perfection
191 idea of best regime/idea of the just social order
V. B: Locke (42 paragraphs)
222 "idea of god"
Chap VI: Crisis of Modern Natural Right
VI. A: Rousseau (44 paragraphs)
253 two classical ideas: city/virtue and nature
261 classical idea of philosophy
292 "idea of the future"
VI. B: Burke (34 paragraphs)
316 idea of History
322 "the very idea of the fabrication of a new government"
Which then are the chapter pairs? The hint is contained in the number of paragraphs:
Chapter I (idea of philosophy) and VI. B Burke (idea of history) (34 paragraphs each)
Chapter II (idea of science) V. B Locke ("idea of god") (42 paragraphs each)
Chapter IV (idea of justice) and V. A Hobbes (idea of best regime) (40 paragraphs each)
Chapter III ("idea of nature") (48 paragraphs) and chapter VI. A Rousseau ("idea of the future") (44 paragraphs)
The final 4 paragraphs of chapter III treat ancient conceptions of "egalitarian natural right," a modern phenomenon.