Let's say Bob insults me and I punch him in the nose. Did Bob cause me to punch him in the nose? Of course not. Just like the Terminator, I scrolled through a list of options, and selected "punch him in the nose". I could have selected "your mother is a hamster and your father smelt of elderberries." I could have selected "do nothing".
What's your definition of cause here? Human agency? In that case, people could have decided to donate part of their salaries to businesses they previously frequented,or other rediculous "choices" that humans would never do.
I don't think there is a coherent notion of cause and effect where both covid does not cause the recession and the lockdown does. I can see very restricted notions of cause and effect where neither "cause" it, and more normak notions where both cause it, but not one where one causes but not the other.
And that's ignoring the absolutely rediculous premise that the covid death toll and long term disability toll has no effect on the economic downturn and it was purely caused by the lockdown. There are reasonable arguments that lockdown has been a net positive for the economy in the long run (even more so for non-usa countries that did it competently)
Why stop there? By that logic the recession is not caused by the lockdown but by less businesses being open and reduced consumer spending.