Estimates for the Size of the Ottoman Fleet Before the Battle of Lepanto
The size of the Ottoman fleet directly before the Battle of Lepanto varies significantly depending upon what source you are looking at. Most authors only give a rough estimate recorded by the Holy League from various sources. In Malcolm’s Agents of Empire : Knights, Corsairs, Jesuits and Spies in the Sixteenth-Century Mediterranean World, he notes four reports of the Ottoman’s fleet before the Battle of Lepanto:
In July 1571, an escaped Venetian slave said that the Ottoman fleet is comprised of 193 galleys and galiots, as well as another 107 smaller ships.

In August 1571, another sources says that the Ottoman fleet is comprised of 180 galleys and 100 other ships.

In August 1571, an escaped Spanish slave said that the Ottoman fleet is comprised of 155 galleys and 80 smaller ships.

Later, another source says that the Ottoman fleet is comprised of 150 galleys and 150 smaller ships.
According to these four sources, the Ottoman fleet stood somewhere between 230 and 300 ships. This wide range even confounded the Holy League, which struggled on what to make of this information. This confusion is shown in Marquis Ascanio della Corgna report to Don Juan, the lead commander of the fleet when he wrote “…and as for the number and quality of the ships in the Ottoman fleet, the reports are so various that I cannot judge very well if it is smaller or greater than ours.”

According to the contemporary, Venetian historian Paulo Paruta in his The Wars of Cyprus, the Holy League’s fleet was recorded at being around 250 ships the day before the Battle of Lepanto. Of these ships, he claims that around 200 were galleys, 6 were galleasses, and the remaining were flyboats.

Today, the general historical consensus is that the Holy League’s fleet was indeed smaller than the Ottoman’s. This claim is supported in Finkel’s Osman’s Dream and Malcolm’s previously cited work. However, the exact number of Ottoman ships is still fuzzy. Therefore, we may consider the Ottoman fleet to have at least 250 ships. But, while the Ottomans had the larger fleet, the Holy League’s fleet was better equipped, better supplied, better manned, and featured Venetian galleasses, which devastated the Ottoman ships.
The Rebuilding of the Ottoman Navy
The Battle of Lepanto was a disastrous defeat for the Ottoman Empire, which was shook to its core. Malcolm recounts a Venetian diplomat’s claim that people in Istanbul were prepared to flee to Anatolia and that the Sultan, Selim II, sent out a flurry of messages to the governors of Greece, that an attack could be imminent. The latter account indicates that the Ottoman navy was indeed in complete disarray – almost completely destroyed – and would not be able to defend the waters around Greece.

Soon after their defeat at Lepanto, during the winter of 1571-1572, the Ottoman navy began rapidly rebuilding. In fact, a navy that could rival the League’s was constructed in about six months, while the Holy League recovered in friendly ports. The first step, however, was to gather any remaining ships, as stated by Malcolm:
One of the Sultan’s first orders, on 28 October, had instructed [Uluç Ali Pasha] to gather all the ships he could find and bring them in the direction of Istanbul; he had managed to pick up 40 more Ottoman vessels from the Aegean islands, which enabled him to make a grand and reassuring entrance into the Golden Horn with a fleet of 87 ships.
Uluç Ali Pasha commanded the Ottoman left wing during the battle and escaped with his squadron. So, we can possibly assume that some of these ships were from the battle. Furthermore, from the 40 vessels collected from the Aegean Sea, we can assume that some combat-worthy ships were not used during the battle or were retrofitted to serve as combat or auxiliary ships. However, it is unclear whether these vessels were galleys, or lighter and lesser-equipped ships. Nonetheless, this marked whatever remained of the Ottoman navy and the beginning of an incredible quick rebuilding period.

The contemporary Ottoman historian, Mustafa Selaniki, details:
With Gods help, without delay, within 120 days, a rebuilt imperial fleet composed of 134 galleys, baştardas and mavnas propelled with scaloccio oars and filled with combatants and weapons and janissaries and members of the bölüks, all able and select warriors, made its appearance at sea by the day of.. spring equinox, this time with such majesty and pomp that experienced intelligent experts became mute when trying to define and explain [this resurrection]: [For], God be praised, through the excellent judgment and measures of the great vizier a task had been accomplished that astounded the enemies of the religion…
This quote is presented in Soucek’s Navals Aspects of the Ottoman Conquests of Rhodes, Cyprus and Crete.

As stated by Selaniki, the Ottomans were able to rebuild their fleet in under six months. The resulting fleet was comparable to the size of the navy before the Battle of Lepanto. However, while the Ottomans were able to rebuild their fleet with surprising speed, it was not tested in any serious manner for the rest of the Venetian-Ottoman War.

In addition, as the contemporary historian Mustafa Ali records:
the blow of the sword has descended upon able captains expert in naval matters, and at least a generation will pass before each one of them is supplanted with a man of similar caliber…
Another problem lied in finding knowledgeable sailors to lead the Ottoman navy. The defeat at Lepanto not only destroyed ships, but also resulted in the deaths of many of the top commanders of the Ottoman navy.
The Untested Ottoman Navy
The 1572 campaign saw a series of naval standoffs between the Holy League and the recovered Ottoman Empire. On several occasions, the two navies met, but both refused to fully commit to fighting one another. This is best characterized by the contemporary Mustafa Ali’s description of Uluç Ali Pasha tactics in 1572:
…the imperial fleet left its harbor in the capital and, consisting of 150 victory-bound ships, was confronted by [enemy] ships off Navarino, but neither side dared to attack the other: The abject infidels because they were satisfied with the gains of the previous year, the warriors of Islam because, remembering the grave defeat they had suffered in that year, gave no sign of mustering courage in their hearts to take revenge. Especially the noble admiral, who had survived the terrible disaster, aware of the fact that the soldiers lacked courage for battle, found a limited display of [the fleets] strength and steadfastness prefer able, and was wary of following, like his predecessor Ali Pasha, the mindless command “You must confront and fight [the enemy under any circumstances]”.
This quote is presented in Soucek’s Navals Aspects of the Ottoman Conquests of Rhodes, Cyprus and Crete.

Thus, it is difficult to determine the efficacy of the newly rebuilt Ottoman navy in 1572 as neither side wished to engage. So, it is difficult to say if the Ottoman navy was actually comparable in quality to the Holy League’s or if it suffered from the same issues that plagued it leading up the battle of Lepanto. These issues being: a lack of artillery, a lack of supplies, a lack of sailors, and a lack of the more modern galleasses.

By 1573, the Holy League had mostly fallen apart and its mostly absent navy posed little threat to the Ottoman’s. Mostly unopposed, the Ottoman navy raided Spain’s Italian holdings. And in the following year, 1574, the Ottoman navy successfully captured Tunis, which was briefly captured by Spain in 1573. However, even with the capture of Tunis, the Ottoman fleet was unchallenged and still largely untested.

Overview
At a conservative estimate, the Ottomans had at least 250 ships in its navy before Lepanto.

Following the fleet’s destruction, Uluç Ali Pasha reportedly collects 40 ships in the Aegean Islands for the new navy, perhaps hinting that a part of the navy was not committed to the battle. However, the quality of some of these ships is hard to determine. 87 ships are mustered in total.

It is difficult to determine if this new navy was competitive with the Holy League’s, because there was not another pitched battle, like Lepanto.