I have never seen HBO’s Rome, but if the events with Lucius Vorenus occur before 18 BCE, disgrace and derision may be likely if no action is taken, but is purely conjecture. (I don’t think it’s logical for me to assume the Lucius Vorenus mentioned in the title is the same Centurion referenced in Caesar’s De Bello Gallico, so I will mention the two important time periods of adultery laws in my area of knowledge.) However, if they happen after 18 BCE, the husband does in fact have the right to kill someone in a few situations, but is not required to give the death penalty. However, the husband may be charged with pandering should he know about said affair, but not act at all upon it. If this is what they mean by disgraced, then perhaps.

Firstly, during the reign of Augustus, the Lex Iulia was created, giving some rights to the male head of the family in situations like this. For instance, the male head of the family (paterfamilias,) has full authority to act out rights laid out in the Lex Iulia. One example of those rights was that if the Paterfamilias finds that his daughter is having adulterous affairs in his household, both of the contenders could legally be killed. (If one, not both are not killed, the Paterfamilias could be charged with murder.) If the Paterfamilias’ wife is found to have had adulterous relations with a non-citizen such as a gladiator, prostitute, actor, or dancer, the husband could kill the outside lover, but not his wife. If the Paterfamilias chose this route, he is legally obliged to divorce the wife, and charge her with adultery within a small amount of time. (Somewhere between 3-5 days from memory, I could not find the amount of days in the text I have available to me.)

Cato the Elder’s speech, On the Dowry, sheds some light on some ideas of where the statement may come from if the events of the show happen before the Lex Iulia, and possibly what may have been in the Lex Scantinia. However, if this is the source of their statement, it is just wrong, as no confirmed source exists of someone legally using Cato's words.

”When a husband divorces his wife, he judges the woman as a censor does, and has full powers if she has committed any wrong or disgraceful act; she is punished if she has drunk wine, if she has done wrong with another man, she is condemned to death.”

”If you should catch your wife in adultery, you may with impunity put her to death without a trial; but, if you should commit adultery or indecent acts, she should not dare to lay a finger on you, nor is it lawful.”

As the only substantiation for arguments saying this is possibly true before the creation of the Lex Iulia is bad wording in Lex Scantinia, (I personally don’t buy this, as the Lex Scantinia focuses purely on penalizing homosexuality.) it seems likely that Cato was purely staging ground for his later use of sexual morality in politics. Besides, the Lex Scantinia was to punish stuprum, or sex crimes, such as debauchery.

Cato is somewhat known for his usage of ‘morality’- he expelled someone from the senate likely of winning consulship in the following election for kissing his own wife in broad daylight with the daughter watching. How scandalous!

To recap: It’s partially true. There isn’t much sourcing to substantiate the ostracizing of the husband if he did not use the rights of the Lex Iulia or carry out the speakings of Cato, there are several instances in which the husband can be charged if no action is taken.

Sources

Plutarch, Life of Cato the Elder

Cato, On the Dowry

Lex Iulia de Adulteriis Coercendis

Catherine Edwards, The Politics of Immorality in Ancient Rome

Suzanne Dixon, The Roman Family