Heat oil in a soup pot over medium. Cook onion and carrot 7 minutes. Stir in garlic, tomato paste and cumin for 1 minute.
Add lentils, broth and salt. Bring to a gentle boil; reduce heat and partly cover. Simmer 20–25 minutes, stirring occasionally, until lentils and carrot are very soft.
Remove from heat; blend smooth with an immersion blender. Rewarm on low if needed.
Melt butter in a small saucepan on low. Stir in mint and paprika for 20 seconds; immediately stir into soup.
Remove soup from heat; stir in lemon juice.