Heat oil in a 6-qt. saucepan over medium-high heat. Add garlic, carrots, celery, and onion; cook, stirring occasionally, until slightly caramelized, 12–14 minutes.
Stir in cumin, chile flakes, squash, salt, and pepper; cook until squash is soft, about 15 minutes
Add stock and lentils; bring to a boil. Reduce heat to medium-low; cook, slightly covered, until lentils are very tender, about 20 minutes. Let soup cool slightly, then, working in batches, purée soup until smooth. Ladle soup into bowls and garnish with parsley and paprika; serve with flatbread and lemon wedges on the side.