Tough to say. A nation-wide lockdown would be unconstitutional. The federal government has a lot of ways to make it happen--denying federal funding to states that don't lockdown, etc--and although it would be found unconstitutional by the courts it could take months for that to happen. A lot of damage could be done in the interim.
But such a measure would not be taken by Trump, it would only come from Biden/Harris. And if Biden wins the election, gare-an-teed the transition to a COVID-free world begins very quickly. We would stop testing asymptomatic people, the media would stop reporting on "cases" (see: positive tests) surging, schools would open up, and blue state governors would suddenly change their tune during Thanksgiving and Christmas, encouraging "safe" gatherings. Shortly after inauguration everything would be back to normal.
I have no idea what will happen if Trump wins. The immediate thought is that the COVID hysteria will continue unabated. But blue state governors and major metro mayors must be looking at their financial and political situations--massive unemployment, people fleeing to red cities/states, kids failing in school because of the disaster we knew online learning would be--knowing they're untenable. It's impossible to think they can keep it up for another four years.