Bring 9 cups of water to a boil in a large saucepan. Stir in the barley and simmer over low heat until tender, about 1 hour. Drain, rinse well with cold water, then drain again and transfer to a large bowl.
Bring a medium saucepan of salted water to a boil. Add the green beans and cook until tender, about 3 minutes. Using a slotted spoon, transfer the beans to a colander and rinse; add to the barley in the bowl. Add the lima beans and corn kernels to the boiling water and cook until tender, about 2 minutes. Drain, rinse with cold water and add to the barley along with the onion. Season the salad with salt and pepper.
In a small dry skillet, toast the cumin over low heat, stirring, until fragrant, about 2 minutes. Transfer to a bowl and add the lemon juice and mustard. Slowly stir in the oil until emulsified and season with salt and pepper. Toss the dressing with the barley salad, cover and refrigerate overnight to allow the flavors to blend. Let return to room temperature, then season with salt and pepper and toss before serving.