Heat oil in heavy large saucepan over medium–high heat.
Add onions, celery, carrots, and garlic; sauté until vegetables begin to brown, about 15 minutes.
Add the broth, lentils, and tomatoes with juice and bring to boil. Reduce heat to medium–low, cover, and simmer until lentils are tender, about 35 minutes.
Transfer 1/2 cups soup (mostly solids) to blender and puree until smooth.
Return puree to soup in pan; thin soup with more broth by 1/4 cupfuls, if too thick.
Season with salt, pepper, and a squeeze of lime juice, if desired. Ladle soup into bowls. Garnish with coriander/cilantro or Parsley leaves.