After further research, I suspect no source other than Derbyshire's text exists. If so, this would be just a very small slip in an excellent and well written text. I know I have made similar slips.
Here is my reasoning. First, Lebesgue published his first paper in 1898, three in 1899 and then two in 1900 (all most easily found in his collected works). None of these contain any references to the prime numbers:
- Sur l'approximation des fonctions, Bull. Sci. Math. 22 (1898), 278--287.
- Sur la définition de l'aire d'une surface, C. R. Math. Acad. Sci. Paris 129 (1899), 870--873.
- Sur les fonctions de plusieurs variables, C. R. Math. Acad. Sci. Paris 128 (1899), 811--813.
- Sur quelques surfaces non réglées applicables sur le plan, C. R. Math. Acad. Sci. Paris 128 (1899), 1502--1505.
- Sur la définition de certaines intégrales de surface, C. R. Math. Acad. Sci. Paris 131 (1900), 867--870.
- Sur le minimum de certaines intégrales, C. R. Math. Acad. Sci. Paris 131 (1900), 935--937.
So if Lebesgue stated that one was prime in 1899, it appears not to be in a published work of his. (This does not rule out lectures, interviews, works written about him by others...)
Second, all of the Internet references to this that we checked either cite Derbyshire, or were posted well after his work. For example, a friend of mine checked Wikipedia, and this statement about Lebesgue and unity appears in the English and Dutch entry for prime, but not the French, German, Spanish, Italian, Portuguese, Polish, Russian, Czech, or Swedish. In English it was added in 2006, after Derbyshire's 2003 text. In English only it is also found in the Wikipedia page for "Henri Lebesgue":
Is this proof Derbyshire's text is the source, absolutely not. Recall Derbyshire said that he can not recall his source, but that there was one. So if you can find a source that predates his text, I'd like to know; otherwise I think it may just have been a small transcription error while written this popular text. I have done the same myself.
As for the related question: who was the last mathematician of any importance who considered the number 1 to be a prime, my student and I settle on G. H. Hardy in our draft paper (http://arxiv.org/abs/1209.2007). Hardy's A Course of Pure Mathematics, 6th edition, 1933, presented Euclid's proof that there are infinitely many primes with a sequence of primes beginning with 1:
(This was changed in the next edition.) As discussed in our draft article, there is even a remnant of Hardy listing 1 as prime in the revised 10th edition of his text published recently.
We have a list of over 125 references pertinent to the question "is one prime" collected here: http://primes.utm.edu/notes/one.pdf
The naturals come from adding 1 a finite number of times to 0. The integers include these and their negatives. Neither of these statements refer to the number base needed to express them as numerals. Then the rationals again are ratios of integers without reference to base.
The equivalence of this definition of rational to terminating or repeating numeral expansions is dependent upon the base being a rational. If you want to write numbers in base $\pi$, it would be natural to write $\pi=10_\pi$, but then $4$ and $9$ which will have "irrational looking" expansions. This is an artifact of using an irrational base.
Best Answer
This is not a complete answer, but too long for a comment. I think that to definitively answer your question would require access to (or knowledge of) both Renaissance era math texts and books/papers from the 1700s (when math in Latin started to be translated to English).
Once upon a time the Greeks used the word "logos" to mean what we think of today as a ratio (a scaling factor; one quantity divided by another). In the 1600's, Greek mathematical text was translated into Latin and the word "ratio" was used for "logos". In Latin, "ratio" meant something that was reasoned out, calculated, or thought through. You can perform all of these actions using logic. But if you are reasoning out, calculating, or thinking through a numerical computation (like evaluating $\frac{a}{b}$), you might have what we today call a "ratio".
So I would say the answer is both. Most recently, a "rational number" is what we today call a "ratio" - it's one number divided by another (specified to two whole numbers). But if you look a little further back in the etymology, the reason that "one number divided by another" is today called a "ratio" is because that happens to be something that you would reason out. And so with that underlying etymology, a rational number is a number that "makes sense" as the end result of some logical thought.
Just because, here are my two other favorite math etymology items.