Yes. In democracy, the public are the arbiters of truth. Particularly political truth.
Free speech doesn’t mean consequence-free speech. Cooling-down periods, mandatory preservation and disclosure requirements, et cetera are both prudent and commonplace. Court-supervised anti-fraud statute, which punishes for the harm done by the lie, not the speech itself, also helps.
Governments should not have the power to silence their critics. It’s a conflict of interest between the rulers and the ruled, and historically marches towards poverty, misery and instability.