It's just an argument that the actual deficiency could cause worse outcome. But that article in Lancet doesn't claim that Italy had Vitamin D deficient population. The number of deaths per capita due to Covid-19 was however orders of magnitude higher in Italy and Sweden than in Germany. I don't think that there's anywhere any evidence that Germans are less Vitamin D deficient than Italians and Germans.

Vitamin D doesn't explain anything related to Covid-19 deaths in Europe, whereas the existence or lack of measures do, almost perfectly. Whoever can look at the curves of number of deaths since the begin of the epidemics, check the times of partial lockdowns or the introduction of some measures, can see that exactly around three weeks after these the curves stop going up and begin going down.

Italy as the first country seriously hit in Europe had the curve raising exponentially up until the measures started to work (there's a delay -- for people to stop dying the spread of infection has to turn first etc). Sweden also had the curve raising comparably to Italy, even if they had a negative example from Italy -- because there was a decision of targeting the "herd immunity". Germany's curve remained very low, as they had low prevalence at the time their measures started to be applied.

It's all about the measures and the adherence of the people to them.