Uh, no.
1. You're way overestimating the wealth of the Near East in the time period we're talking about. If you look at Maddison's estimates of historical GDP (e.g., https://en.wikipedia.org/wiki/List_of_regions_by_past_GDP_(P...), you can see that circa 1000, "Western Europe" had a GDP of about 10.9 billion (1990) USD, slightly below "West Asia's" 12.4 billion. But by 1500, Western Europe has ballooned 44.2 billion, while West Asia has fallen to 10.5 billion.
2. Italian merchants had regular access to the Near East throughout the Middle Ages and Renaissance, so "suddenly the West had easy access to trade with the East after Lepanto" is not even remotely true.
3. Lepanto's significance even in the context of the 16th Century Mediterranean is highly debatable; arguably, the most it did was to halt further westward expansion by the Ottomans, while they solidified their hold over the Eastern Mediterranean (they did, after all, rebuild their fleet within a year). See, e.g. https://www.historytoday.com/archive/head-head/how-important...
4. The most significant transfers of "knowledge" happened earlier, during the 12th Century Renaissance (translation of Arabic works and Arabic translations of Greek works) and the Italian Renaissance (translation of additional Greek works); continued transfer is evident in the apparent presence of 14th and 15th Century Arabic mathematical and astronomy texts in early 15th Century Italy, where they influenced Copernicus. And, of course, the transmission of other forms of knowledge and technology (compasses, paper, new agricultural products like citrus fruits, rice, and sugar, etc.) occurred throughout the period.