No, don't lie to the public. That's what happened in the first place. "Pfft... you don't need masks." The government said that because masks were hard to get and they wanted to control public behavior. This turned out to be a lie, everyone found out, then regardless of whether the authorities were giving good, accurate advice or not, the trust had been breached.

Politicians saw this as an opportunity to gain ground. In the absence of any trusted authority it became an us vs. them thing for too many people.

Don't lie to the public. Tell them the truth, tell them what they ought to do, and why you think so. Earn trust. It'll be easier to get people to do the right thing.