Use the shredding blade of the food processor to shave the Brussels sprouts into thin pieces; you may have to work in batches. Or slice them thinly crosswise by hand.
Transfer the sprouts to a large bowl and add a large pinch salt. Gather handfuls of the shreds together, rubbing, lifting, and separating them until the salt is distributed and the shreds soften a bit.
Add the olive oil, lemon juice, onion, and a generous sprinkle of pepper. Toss thoroughly and refrigerate for at least 1 hour or up to 6. Taste and adjust the seasoning, adding more lemon if you like, and serve cold or at room temperature.