regarding this lancet article, i will acknowledge that the findings are preliminary, and also maybe wonder if they're asking the right research question.
when i suggested that closing schools might be a good idea, what i was mostly concerned about was transmission to older teachers, and, in the post-secondary context, to aging professors. what these preliminary studies seem to be concerned about is the prevalence of the spread amongst the children, rather than the impact that such spread might have on faculty, which is the real concern with this actual virus due to it's different demographic footprint.
see, they based all their studies around influenza, apparently, which has a relatively high mortality rate in very young people, that levels off in early adulthood and kicks back in again with the elderly. especially virulent flu viruses can also target young, healthy people. so, you definitely want to limit the spread of influenza in children, because they're vulnerable to it. this coronavirus that is causing covid-19 appears to have a very low mortality rate in almost everybody under 60; it is really almost exclusively targeting the elderly, although i need to warn that this might drastically change as it sweeps through the midwest. so, if you're looking specifically for the signals associated with influenza in young people, and you conclude that they aren't well-reflected in covid-19 data, you can kind of trick yourself into missing the point, which is that you want to conduct your studies around covid-19 assumptions rather than influenza ones.
so, i'd like to see some more studies done on this, but my immediate reaction is that it is probably right to conclude that shutting down public elementary schools likely did little to prevent spread in the under-60 demographic, even if it hasn't paid enough attention to the more pressing question as to whether opening certain types of schools (like universities, and high schools) may substantively increase the likelihood of older faculty and staff getting infected.
https://www.thelancet.com/action/showPdf?pii=S2352-4642(20)30095-X