Does the U.S. constitution grant a right to lie? That's what Exxon is arguing in court

Does Exxon Mobil have a constitutional right to sow doubt about climate science? That’s the subject of a high-stakes legal battle playing out between dozens of state attorneys general, members of Congress, corporate executives, and activists.

Last fall, investigations by Inside Climate News and the Los Angeles Times revealed that the oil giant has decades of internal documents showing that its own scientists and executives knew fossil fuels contributed to climate change. Publicly, the company argued that the threats posed by global warming were far from certain, presumably as part of an effort to fight off regulations.

The revelations have sparked a barrage of legal actions. The attorney generals of Massachusetts, California, and New York launched investigations of Exxon, while Democratic AGs from other states have expressed their support. Some have drawn parallels to the tobacco industry’s deception on the dangers of smoking. Exxon has countered that the investigations are unconstitutional and has filed motions asking courts to block the subpoenas. “This…is about freedom of political speech,” the company recently argued in the Massachusetts case.

http://www.wired.com/2016/07/exxon-fighting-right-deny-climate-change/

Yes, the professional cretins that will 'sell their souls & sheepskin degree' for that all mighty   has been something that we were made well aware of during those Big Tobacco trials of the 60's & 70's; sadly, the same things happen even in this, the 21st century. 
Having a 'Degree', even a Masters Degree won't guarantee that the name behind the framed certification is of a solid moral fiber
Now the Big Oil is whining and trying to use 'Freedom of Speech' as their rational for doing their underhanded deception work

OP wrote:Does the U.S. constitution grant a right to lie? That's what Exxon is arguing in court

It depends on whether (1) the lie transgresses any federal, state or city/county law.  Eg, if you lie to a police officer you can be hit with an obstruction of justice or, on the federal level, lying to a federal agent charge.  Mislabeling products and medicines can expose one to criminal charges.  Wire and mail fraud are another type of example.  Certain types of general fraud and deceit actions are criminal, such as bunko and criminal misrepresentation.

The parallel in civil law is any material misrepresentation that causes injury or damage can be grounds for recovery.  If the lie is negligent, then it is negligent misrepresentation.  If it is purposeful, then it is intentional misrepresentation.

And of course, if you lie under oath, as the tobacco companies did, then you are in for perjury charges, some of which are felonies.

Exxon is trying to argue political speech, which brings it into the ambit of the higher bar of the First Amendment. Of course, any scientific statement is corrigible, Scientific methodology is built on the notion that all knowledge will change as we learn more. Conservatives in the political arena have seized on this and made a stand (in this issue) on grounds of scientific corrigiblity, claiming that the findings are inconclusive. But the evidence is pretty overwhelming.

I believe Exxon is trying to piggy-back onto the general principle of scientific corrigiblity, arguing that it has become a political argument. Therefore, they have a right to make their claims...and presumably protect their documentation.