The three justices that dissented from the decision striking down the Stolen Valor Act were Alito, Scalia and Thomas. But when it comes to lying in connection with political discourse, I doubt they'd reach the same conclusions given how it might be used against their political allies.
The six justices that concluded the Stolen Valor Act was unconstitutional included a plurality consisting of Kennedy, Ginsburg, Roberts, and Sotomayor, with a separate narrower opinion concurring from Breyer and Kagan.
The plurality opinion went to lengths to distinguish different categories of speech and the rationale for criminalizing false statements in some situations but not others. A key statement from that decision, which I believe Jackson, Kagan and even Sotomayor would agree, and which Roberts signed onto, makes the following point: "Our constitutional tradition stands against the idea that we need Oceania’s Ministry of Truth. See G. Orwell, Nineteen Eighty-Four (1949) (Centennial ed. 2003). Were this law to be sustained, there could be an endless list of subjects the National Government or the States could single out." And that same opinion made another point that is part of longstanding Constitutional jurisprudence:The remedy for speech that is false is speech that is true. This is the ordinary course in a free society. The response to the unreasoned is the rational; to the uninformed, the enlightened; to the straight-out lie, the simple truth. See Whitney v. California, 274 U.S. 357, 377 (1927) (Brandeis, J., concurring) (“If there be time to expose through discussion the falsehood and fallacies, to avert the evil by the processes of education, the remedy to be applied is more speech, not enforced silence”). The theory of our Constitution is “that the best test of truth is the power of the thought to get itself accepted in the competition of the market,” Abrams v. United States, 250 U.S. 616, 630 (1919) (Holmes, J., dissenting). The First Amendment itself ensures the right to respond to speech we do not like, and for good reason. Freedom of speech and thought flows not from the beneficence of the state but from the inalienable rights of the person. And suppression of speech by the government can make exposure of falsity more difficult, not less so. Society has the right and civic duty to engage in open, dynamic, rational discourse. These ends are not well served when the government seeks to orchestrate public discussion through content-based mandates."
I think that Alito, Thomas, Kavanaugh, Gorsuch and Barrett would point to that principle as a way of ruling against any attempt to criminalize political discourse.
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