Bad logic.
No it is not, or at least the first sentence is perfect logic. You can not decide if an action like this worked without a control group, and we currently are not far enough into this giant experiment for the data to have fully come in. So we have no way of knowing if the lock downs did anything.
Great example of why you need a control group is with the Polio vaccine when they tested it in the 1960s. The initial test preformed though out the USA with 2nd graders required school districts to set up a control group to compare the results to. Most school districts broke up the students whom they received parental permission to perform the test on into two group, one who got the vaccine and one that got a placebo. In this instance, it showed that the vaccine worked, and worked well.
However, some school districts decided to give the vaccine to all students they received parental permission from and just decided to compare those results to the students whom they did not get permission to include in the test. In this instance, it showed the vaccine had no effect what so ever. Seems strange, and it took researchers 40 years to figure out why this discrepancy existed. In short, it was due to an improper control group.
Insofar as my second sentence, that is my personal opinion which I am not really using logic for. But, if you look at the fact that 60% of fatalities occurred in nursing homes, it is kind of obvious the lock downs were overkill.