Stir lemon juice into a large bowl of cold water.
Peel sunchokes and cut into 1/2-inch-thick rounds. Transfer as cut to acidulated water (to prevent discoloring).
Bring vinegar, sugar, water, mustard seeds, turmeric, cayenne, and 1 1/2 tsp salt to a boil in a medium nonreactive saucepan, stirring until sugar has dissolved. Cool brine to room temperature.
Cook sunchokes and onion in a large pot of boiling water 1 minute. Drain and spread out on a kitchen towel to cool. Put vegetables in a glass or ceramic bowl and pour brine over them. Weight vegetables with a small plate to keep submerged, then cover bowl tightly. Chill, stirring once or twice a day, at least 1 week (to allow flavors to develop).
Pickles can be chilled up to one month.