Make the dressing: In a large bowl, whisk together the oil, vinegar, shallot, capers, mustard, salt, and several grinds of black pepper. Transfer half to a small airtight container and refrigerate for later use.
Cook the lentils: Bring a medium pot of salted water to a boil. Add the lentils, reduce the heat to medium-low, and simmer, uncovered, until the lentils are just tender but still have a slight bite, 12 to 15 minutes (don’t overcook — they can turn mushy quickly!). Drain and return to the pot. Season with salt to taste, then let cool.
Assemble the salad: Add the cooled lentils and the chickpeas to the bowl of dressing and toss to coat. Add the cucumbers, feta, olives, sunflower seeds, parsley, 1/2 teaspoon salt, and several grinds of black pepper and toss again. Season with salt to taste. If the salad seems dry, drizzle with a bit of the reserved dressing. Cover and refrigerate until ready to serve.
Toss and serve: Combine the radicchio and romaine in a large airtight container. Refrigerate. When ready to eat, toss together equal amounts of the lentil salad and greens (heaping 1 cup of each). Drizzle with the reserved dressing.
