A blog from 2012:
History reverberates with rumors that the Borgias-father, son Cesare and daughter Lucrezia–committed incest. The Italian aristocracy hated the Borgias and loved to start nasty rumors about them. In my RealHistory e-mystery, A Borgia Daughter Dies, I do my best to sort rumor from fact and fiction, showing the source of the incest rumors, and why I don't believe them.
Showtime could have taken the high road and avoided the rumors all together, since they are unlikely to be true. (See http://maryannphilip.com/cesare-borgia-pope-alexander-vi-lucrezia-borgia-involved-incest/). But judging from the preview to the third season, it appears Showtime is taking the lowest of low roads: pretend there was incest, and blame it on Lucrezia. This is blaming the victim in the story.
The Borgia men did some very bad things–I've blogged about a number of them. In contrast, the worst we know about Lucrezia is that she may have had a baby out of wedlock. As A Borgia Daughter Dies shows, the probable father is known and it was not a family member, much less the fictional Paolo from the Showtime series. (See above post; also see http://maryannphilip.com/lucrezia-borgia-pregnant-convent/) .
The historical record shows Lucrezia as a charming and intelligent woman who was an excellent administrator–the pope actually made her governor of Spoleto, where she instituted various reforms, and had her running the papacy at one point. It seems unlikely he would extend this level of trust to her if he were sexually abusing her. She eventually became known as "the good Duchess" and was widely admired for her good works. Why pick on her?
Guilt by association is probably inevitable for the one good person in a bad family. Lucrezia's bad rep likely stems from a Donizetti opera, written several hundred years after she died, which (like most operas) bears no resemblance to historical reality. She has been labeled a poisoner, but no contemporary or historian has ever identified her supposed victim(s).
In contrast, Cesare, Juan and the pope were surrounded with corpses. The pope regularly put enemies in the Castel Sant'Angelo, from which they soon emerged feet first, without a mark on them. This is how he got labelled a poisoner. Though he may not always have deserved the label (see for example http://maryannphilip.com/borgias-kill-prince-djem/), at least we can see where it came from.
If you want to learn the real story of the Borgias in a fun way, check out A Borgia Daughter Dies, which has persistently gotten 4 out of 5 stars on on Amazon, after 160+ reviews. It's also available on Apple ibooks, and for Nook on Smashwords.