Mash avocado, yogurt and 1 Tbsp. lime juice together in a bowl until well combined but still a little chunky. Season with salt.
Combine white beans, lemon juice, 2 Tbsp. olive oil and garlic in food processor and process until smooth. Season with salt. Scrape into a second bowl.
Combine black beans, remaining 2 Tbsp. olive oil, remaining 2 Tbsp. lime juice, chili powder, cumin and salt in food processor and process until smooth. Scrape into a third bowl.
Serve 3 dips with tomatoes, carrots, pita wedges and celery, if desired, for dipping.
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