1. Preheat oven to 425 degrees. Place barley in a pot and add water to cover by 1 1/2 inches. Bring to a boil, reduce heat and simmer uncovered until barley is tender and water is absorbed, 40-45 minutes. Spread barley on a baking sheet to cool.
2. While barley is cooking, toss fennel slices and 2 Tbsp. of oil in a bowl. Season with salt. Spread fennel slices onto a baking sheet and roast until crisp tender and beginning to brown, about 18 minutes.
3. Whisk orange juice, lime juice, shallot, dill and zest in a bowl. Gradually whisk in remaining 1/2 cup of oil. Season vinaigrette with salt and pepper.
4. Transfer barley to a large bowl. Add Roasted fennel, sliced radishes, olives and dill sprigs. Drizzle in orange vinaigrette to coat. Season with salt and pepper.
Note: Steps 1 and 2 may be done ahead.