Texas and other states did have what were called "paramour laws" back in the day, that day being pre-Civil War in Texas. I just Googled to learn that this "heat of passion" crime was codified as Article 1220 of the 1865-1857 Penal Code. It was repealed in 1974.
Legislative Reference Library | Collections | Codes of 1856
From Eugene Volokh/
The Volokh Conspiracies 2007 :
Until 1974, when it was repealed, [a] Texas statute provided:
Homicide is justifiable when committed by the husband upon one taken in the act of adultery with the wife, provided the killing take place before the parties to the act have separated. Such circumstance cannot justify a homicide where it appears that there has been, on the part of the husband, any connivance in or assent to the adulterous connection.
... Although an early case established that the statute permitted the husband to kill his wife as well as her paramour, Texas courts criticized this interpretation and reversed it the following decade [in 1925]. Furthermore, Texas judges refused to extend the statute to permit a wife to kill her husband's paramour. Under the Texas statute, the injury to the paramour was only justifiable when inflicted with the intent to kill [as opposed to, in one case, castrate]....
The Volokh Conspiracy - The Unwritten Law, Written:
