Bring a saucepan of salted water to a boil. Fill a bowl with ice water and set aside. Using a mandolin slicer or very sharp knife, slice the beets into paper thin slices. Drop them into the boiling water and cook until softened but still firm to the bite, about 5 minutes. Transfer the beets to the ice water with a strainer and cool completely. Lay the slices out on a paper towel-lined plate to dry.
Meanwhile, bring the maple syrup and vinegar to a boil in a small saucepan over medium-high heat. Continue cooking until the liquid has large thick bubbles at the top and the liquid has reduced to about 1/4 cup. Remove from heat, squeeze the lemon juice into it and stir. Be careful – it is extremely hot! Let the mixture stand until cool.