The earliest case I can document for sure, at the very least for the period I study, of someone who read while using the toilet is king Philip II, who was very well known to be a voracious reader, in the words of the great historian Geoffrey Parker. Some explanations are going to be necessary in order to justify my assertion.

In modern Spanish, there is the word "retrete", which is used to mean the toilet, though in the 16th and 17th centuries it had a different meaning, it being a retired chamber, the most private one, as explained by Sebastián de Covarrubias, who I am going to quote and translate:

RETRETE. el aposento pequeño y recogido en la parte más secreta de la casa, y más apartada, y así se dixo de retro.

Translation: RETRETE. The small and secluded chamber in the most secret and farthest part of the house, and it is called that from retro.

In this "retrete", or "retreated chamber", king Philip II had plenty of strictly personal stuff, only available to him and the mozos or grooms charged with keeping everything in proper order and well provided. In this retrete, he had also plenty of books, dozens of them, for his own study or amusement. Let us not forget his accounting shows an unusually high spending in candles, as the king would be up reading, studying laws, decrees, and administrative matters until very late at night, always supervising and micromanaging every single thing produced by the many Councils of the monarchy. He had some really interesting books in his retrete, among them Machiavelli's works, Pico della Mirandola's works, and even some books by Johannes Reuchlin the cabalist.

In this retreated chamber the king would also answer nature's call, as privacy was absolutely assured. I will justify this assertion quoting Gonzalo Fernández de Oviedo's Libro de la Cámara del Serenísimo Príncipe Don Juan, where he describes the retrete and the office of the mozo del bacín, which is to say "groom of the stool" in English terminology:

In the retrete there was a chamber pot made of silver, where the prince would sit in order to do what cannot be excused, but as accessory. This is a particular office of the mozo del bacín[...]

Though Gonzalo Fernández de Oviedo served decades prior to king Philip's reign, the palace etiquette on this matter was not substantially different. There were still mozos de cámara, a mozo del bacín, and the king would answer Nature's call in the most private or retreated part of the palace. Furthermore, when Philip was prince, two extra grooms were added to the palace etiquette in 1537.

Of course, sources are not abundant on these scatological matters. However, with the elements we know, we can safely assume that king Philip II did read while in the toilet. Of course, this is in the time of the printing press, when books could be readily available, and even cheap, so it would not be out of place to have some reading material in the retreated chamber.

Another example of 'retreated chamber' in the 16th century, but from Eastern Asia: Famous Warlord Shingen Takeda (d. 1572) is said once to built the special water closet for his routine business in the 1560s.

"Perhaps for the sake of a measure of precaution, Lord Shingen made his retreated chamber in Kyoto Style of 6 tatami mat size (about 9.5 square meters) to be built. Paved with tatami mat and with the drainage facility making use of the drainage from the bathing building to flush the unclean, the room was burned with incense in the incense burner with crushed agarwood put in the box. It was also said that two appointed pages filled new incense three times in a day, in morning, at noon, and in evening. In addition to that, the only one person was allowed to bring to documents in the chamber, arranged by county and order. That's how Lord examined (read) the documents, considered and further, made a decision in the chamber.....Lord also said that this chamber was just like the mountain [the unshakable power base?] (Clumsy translation is mine. Original Text, Kōyō Gunkan（『甲陽軍鑑』）, Book IX-23 (p.273 in this edition), can be referred to this digitalized edition offered by National Diet Library of Japan). "

One reservation should be mentioned, however: "retreated chamber (閑所)" in early modern Japan (16th and 17th centuries) could sometimes also mean the private room for the ruler in a more general sense, such as the reading room. To give another example, another famous Warlord Masamune Date (d. 1637) was also known to make it rule to pend about an hour everyday in the "retreated chamber" after his breakfast and dinner for thinking, according to the memoir of Shigezane Date (『政宗記』）. Shingen's rival, Warlord Kenshin Uesugi (d. 1578) was also said to fall sudden ill in the "retreated chamber", but some scholars raise objection about their cases of identifying "the retreated chamber" with the rest room. Only for the case of Shingen we fortunately knew with ease that it was clearly the (water) flush toilet thanks for the description of its attached drainage.

(Edited) proofreads a translation (though only a little).