A Columbia professor is arrested for incest — but isn't there a constitutional right to incest between consenting adults?

Here's the news about the professor, David Epstein, who is accused of having a sexual relationship with his 24-year-old daughter. Now, let's read Justice Scalia's dissenting opinion in Lawrence v. Texas (the case that found a substantive due process right to engage in sodomy). Justice Scalia quotes the majority opinion (and adds italics):

“[W]e think that our laws and traditions in the past half century are of most relevance here. These references show an emerging awareness that liberty gives substantial protection to adult persons in deciding how to conduct their private lives in matters pertaining to sex.”

Scalia then writes (and I'm adding the boldface):

Apart from the fact that such an “emerging awareness” does not establish a “fundamental right,” the statement is factually false. States continue to prosecute all sorts of crimes by adults “in matters pertaining to sex”: prostitution, adult incest, adultery, obscenity, and child pornography. Sodomy laws, too, have been enforced “in the past half century,” in which there have been 134 reported cases involving prosecutions for consensual, adult, homosexual sodomy..... In relying, for evidence of an “emerging recognition,” upon the American Law Institute’s 1955 recommendation not to criminalize “‘consensual sexual relations conducted in private,’ ” the Court ignores the fact that this recommendation was “a point of resistance in most of the states that considered adopting the Model Penal Code.”....

The Texas statute undeniably seeks to further the belief of its citizens that certain forms of sexual behavior are “immoral and unacceptable”... the same interest furthered by criminal laws against fornication, bigamy, adultery, adult incest, bestiality, and obscenity. Bowers held that this was a legitimate state interest. The Court today reaches the opposite conclusion. The Texas statute, it says, “furthers no legitimate state interest which can justify its intrusion into the personal and private life of the individual” ... The Court embraces instead Justice Stevens’ declaration in his Bowers dissent, that “the fact that the governing majority in a State has traditionally viewed a particular practice as immoral is not a sufficient reason for upholding a law prohibiting the practice.” This effectively decrees the end of all morals legislation. If, as the Court asserts, the promotion of majoritarian sexual morality is not even a legitimate state interest, none of the above-mentioned laws can survive rational-basis review.

Of course, the Court did assert that in Lawrence, so according to Justice Scalia, under the existing precedent, consensual adult incest cannot survive rational-basis review.