Surely a secondary effect of lockdown has to be its impact on public health, by way of delayed treatments, people avoiding doctors and hospitals, mental health issues from destroyed livelihoods etc., etc.
Absolutely not. The question depends on the difference between locking down when appropriate and not doing so.
If lockdown had been started when appropriate (mid February) there would have been
no cases to block hospital beds. There would have been
no cases to infect hospital staff so that services had to be laid off. There would have been
no cases to infect people attending hospital for other conditions so healthcare could have continued normally.
So the effect of delaying lockdown is entirely negative on public health. The effect lockdown is positive.
Once it is too late lockdown has no impact on making healthcare more difficult. Lockdown itself did not include blocking hospital services. It always allowed people to access healthcare if they need to - that has been explicit. Accessing healthcare has been blocked purely because of the effects of delaying lockdown - making it impossible to get things to work.
Lockdown has had no negative effects on mental healthcare. If it had not been instituted the situation for mental health would have been
worse. If it had been instituted earlier no mental health problems would have arisen. Similarly for livelihoods. Livelihoods had some chance of recovery
once lockdown had worked. The ridiculous thing is that the easing of lockdown included measures that ensured it all had to be done again. If lockdown had been instituted in time the only industry to suffer would have been airlines and tourism. It would have cost relatively little to support these- which we probably ought have trimmed down anyway for climate reasons. As it is the cost of supporting almost all non-essentia business is going to be eye-watering.
Lockdown did not cause ANY OF THESE PROBLEMS.
The virus caused all these problems. Lockdown made things tolerable again for a while. When considering what is caused by X you have to consider
what would happen without X - and the answer is that all these things would be far worse - so X did not cause the problems.