Stir coriander in small skillet over medium heat until fragrant, about 4 minutes. Cool. Coarsely grind coriander in mortar with pestle or in spice mill. Add vinegar, garlic, salt, and pepper. Whisk in oil.
Puree first 9 ingredients in blender until smooth. (Can be made 1 day ahead. Cover and chill. Reblend before continuing.) Whisk in lime juice.
Preheat oven to 350°F. Wash and dry beets. Cut off beet greens 1 inch from top of beets; reserve for another use. Rub beets with oil. Place light-colored beets in 1 roasting pan and red beets in another; sprinkle with coarse salt. Cover pans tightly with foil. Roast until beets are just tender, about 55 minutes. Cool slightly. Rinse under cold water and rub off skin from beets. Cut beets in half. Toss beets in bowl with 4 tablespoons vinaigrette. Let stand 30 minutes. Toss lettuces in bowl with some of vinaigrette to coat lightly; divide among plates and top with beets. Drizzle pesto around salads and serve. Beets may be steamed instead of roasted for a quicker fix. Steam until fork tender.