Yes it can. Labs specifically study, and propagate, mutations. A lab can do in years what might take nature decades. If it did originate from a lab, we very likely would never find a close enough progenitor in nature to know where things started (what strain the lab started with).
There is a probabilistic aspect to this though. If we happen to find the exact wild virus population Cov-19 originated from (whether it then mutated naturally or in a lab) then I think we'll nail it. On the other hand if we just find an adjacent population that diverged from the actual Cov-19 source some time ago it could be harder to pin down the route.
It's not a recipe to create virus in a lab. It's a recipe to manufacture copies of the virus in a lab.