Why is Renzo the protagonist instead of Lucia?

In this book, both Renzo and Lucia are the protagonists. They are equally important and have the same goal. Renzo is perhaps talked of more in the book, having more of an active role in the movement of the plot. Lucia, however, plays just as vital a role.
Although this book is told as a love story, it is also viewed as a veiled attack on the Austrian Empire, which controlled the region of Northern Italy when the novel was written. It is also favourably viewed by historians for its extraordinary description of the plague that broke out in Milan at the time.
Most interesting in relation to your question is the inclusion of Lucia as an active protagonist. At the time very few books included much about women, even as main characters. However, Lucia is given a very active role and a detailed description. She is, like many depictions of women in that time period, a kind and pious young woman, but she is not all good. She can also be cruel and self-centered. Another interesting inclusion is the character of La Monica di Monza (or the Nun of Monza), who is depicted as a bitter, frustrated, and somewhat ambiguous woman with a dark past, who befriends Lucia. This character was based on an actual woman, Marianna de Leyva.
The author, Alessandro Manzoni, was beyond a doubt ahead of his time with his depictions of real and honest characters and his inclusion of women of all types and backgrounds in his novel. It is little wonder that this book has been called the most widely read novel in the Italian language.