The Ohio court viewed Lawrence as a simple rational-basis decision. This seems to be the view of most post-Lawrence decisions, but it is by no means clear from the Supreme Court's poetic but legally muddled opinion.
If only rational basis review applies, it's pretty clear that Ohio's incest ban survives. It is rational to conclude that incestuous relationships may have destructive tendencies even between consenting adults. To the extent that this danger may sometimes be lessened with stepparent relationships, the stepparent who has not adopted his stepchild may get outside the ban by divorcing.
It is less clear to me that this law would pass muster if a fundamental right were involved, for it is at least arguable that the dangers of incest are less pervasive and less severe when with consenting adult. This would present a complex question, begging some illumination from the social sciences. But since the law was upheld, a narrowing amendment by the legislature is at least worth considering carefully in light of the serious criminal consequences (not that it will happen, of course).
Interestingly, in this case a dissenting justice said nothing of the constitutional issue but took issue with the court's statutory interpretation, based on a different reading of the legislative history. He went on to say:
I suspect that the statute was not employed in this case as a means to preserve Ohio’s fractured extended families. Rather, the state used [the law] as a means to prosecute a strict-liability, slam-dunk sex offense that does not allow the defendant to present any evidence regarding the consent of the victim. [The incest law] provides a shortcut to a conviction. This sort of use of the statute demeans its true purpose.This is a problem that has often occurred to me, and which I had not yet seen recognized by courts. There is no indication from the opinions whether consent was in any way doubtful in this case. But I suspect that this is a major reason why many laws criminalizing consensual sex are kept on the books. To use laws like this as a "shortcut to a conviction" would seem to erode the basic rights of the criminal defendant and cheapen our system of justice, even if it sometimes helps put bad guys in jail.