I haven't gone over it thoroughly but it seems to me that there are more than a few flaws. Not least, the focus on the worst-affected countries seems a little difficult to justify: would it not be appropriate to consider countries where lock-down was implemented earlier in the disease's growth curve? Is there a point where the intervention measures are, perhaps, "too late" to have a major effect? What happens if the intervention was brought in earlier?
The focus on death statistics is also somewhat problematic because these are still being updated. Today's round of NHS England updates, for example, added a few deaths from towards the end of March. Even leaving those problems aside, the author's "pre-lockdown projections" in eg Figure 4 seem wildly optimistic, both in the choice of function and in the parameters. Consider, for example, the claim that without interventions the Covid-related death number in Italy would have dropped to zero by about two weeks ago. Presumably this is meant to represent an optimistic scenario but must come with a huge uncertainty that appears to have been not taken into account, in the presentation of the data if not in the processing. Otherwise it is simply unsustainable to make this claim.
I'm sure I could think of other criticisms. One that is more than suggestive is the number of typos, which in itself doesn't undermine the work but does show that the work has been rushed a little and not already examined by somebody else prior to preprint. Coupled with the fact that it's not been subject to peer review, it could seriously benefit from an outside voice asking questions.
Oh, yes, and it's a paper from someone outside the specialism. Again, in itself that doesn't undermine the paper, but it gives pause for thought: does the author have the experience needed to analyse these data in this context in a sensible way? I'm not an expert in epidemiology or anything close to it, and I wouldn't presume to write a paper questioning the efficacy of public policy with so little background in the field.