1. Combine wheat berries, 1 onion half, thyme sprigs, and 1 tablespoon salt in a large saucepan; add water to cover by 2 inches. Bring to a boil; reduce heat to medium and simmer until wheat berries are just tender but still firm to the bite, about 35 minutes. Drain; discard onion and thyme. Place wheat berries in a large bowl; let cool.
2. Cut remaining 3 onion halves crosswise into 1/2-inch slices. Heat 1tablespoon oil in a large pan over medium-high heat; add onions. Season lightly with salt and pepper. Cook, stirring occasionally until onions are charred in spots, about 5 minutes. Transfer to bowl with wheat berries. Add 1 tablespoon oil to same skillet. Working in 3 batches, add kale and cook, tossing occasionally, sprinkling with salt and pepper, and adding oil as needed between batches, until charred in spots, about 1 minute per batch.
3. Add charred kale to bowl. Drizzle with lemon juice and any remaining oil; toss to coat. Season to taste with salt and pepper.