Transfer the cooked onion mixture to a blender or food processor and add the black beans, salt, cumin, lime juice, water and cilantro. Blend until smooth (if you're using a blender, you may need to stop and stir a few times to help it out). If the dip is too thick, add more water or lime juice, little by little, to thin it out. Taste and adjust seasoning, then transfer to a serving bowl. Serve warm, cold or room temperature with tortilla chips.