I think Lewis's contention in that essay is wrong, because he confuses two claims.
The second of these may well lead to the conclusions he deplores (e.g., that there's no such thing as too harsh a punishment, if it has the effect of deterring and/or reforming). The first doesn't, because there can be other constraints on punishment. (E.g., it seems to me perfectly consistent to hold that what punishment is for is deterrence and reform, but that it is wrong to inflict any punishment more severe than some limit derived from the severity of the offence being punished.)
I think (some) people believe that the sole functions of punishment are deterrence and reform in the same way as they believe that the sole function of cancer surgery is to remove tumours; that doesn't commit them to accepting limitlessly harsh punishment in the pursuit of reform, any more than it commits them to having cancer surgeons remove so much non-cancerous tissue that they kill their patients.
The first doesn't, because there can be other constraints on punishment.
There can be, but but the theory he is opposing knows only these two, constrained only by their production of collective welfare, just as the cancer surgeon cuts out tumours as required for the patient's health. A metaphor that excellently conveys Lewis' horror at what he calls the humanitarian theory. The committers of bad deeds are a cancer to be cut out. Their status as people does not weigh in the scales. The collective is all.
Lewis is arguing that while these two things matter,...
Another month, another rationality quotes thread. The rules are: