Since the Great Depression started before Smoot Hawley tariffs were intoduced and the Stock Market Crash happened long before the bill that eventually became law had its details ironed out the lesson is a false lesson.
I'm no big fan of free trade, and I don't know whether free trade could have cured the Great Depression. Roosevelt's policies certainly didn't. But closing down markets with high tariffs was probably the wrong response to hard times.
Those who lived through the Depression and came to power after the war certainly drew that conclusion, and the argument that free trade makes recessions (and maybe inflation, too) milder is one that protectionists will have to take seriously.