Lawrence is notoriously inscrutable in this regard, and has thus been a vexing case for constitutional law professors to teach. [One suspects Amar has been one of those vexed professors!] The Ninth Circuit panel argued, interestingly, that this linguistic inscrutability should lead us to focus on the Court’s result in Lawrence, rather than just on what the Court said in reaching that result. As the Ninth Circuit put the point, “[i]n these ambiguous circumstances, we analyze Lawrence by considering what the Court actually did, rather than by dissecting isolated pieces of text. In so doing, we conclude that the Supreme Court applied a heightened level of scrutiny in Lawrence.”
While the inscrutability of Lawrence is perhaps an unusually pointed example, courts often puzzle over just what the holding of a decision is, sifting through sometimes seemingly inconsistent bits of an opinion. The Witt panel's function approach seems to me to be a faithful application of the distinction between ration decidendi and obiter dicta: when the text of a binding opinion is ambiguous as to its rationale, look to the holding the court reached and how it got there. In Lawrence, the Court got there by criticizing Bowers v. Hardwick for misunderstanding the nature of the privacy right involved, and citing decisions that applied heightened scrutiny. In fact, most of the Court's reasoning would have been dicta if it were applying rational-basis review. This is not a self-evident, unassailable approach, but it makes more sense - simply as a matter of how to apply a confusing precedent - than anything else I've seen on Lawrence.
Amar also correctly notes that the Supreme Court is likely to ultimately decide the DADT issue -- if, and it's a big if -- the political branches don't chuck the policy first.