Heat coconut oil in a pot over medium-high heat. Saute onion in hot coconut oil until softened, about 5 minutes. Stir tomato paste and garlic with the onion; cook and stir until the garlic is fragrant, about 2 minutes more.
Sprinkle flour over the onion mixture and stir to incorporate; add vegetable broth, crushed tomatoes, chopped basil, lemon juice, maple syrup, and bay leaf. Bring the broth to a boil, reduce heat to medium-low, and cook at a simmer until the tomatoes are completely softened, about 20 minutes.
Turn heat below pot off. Remove and discard bay leaf. Pour soup into a blender. Hold lid in place and pulse blender a few times to get mixture moving before leaving on to blend into a puree; pour pureed soup into the pot and place over medium-low heat.
Stir coconut milk into pureed soup until the color is consistent; heat until the soup is warmed. Season soup with sea salt and garnish with fresh basil sprigs.