Combine baby spinach and carrot in a food processor; pulse until finely chopped.
Heat oil in a large pot over medium heat. Cook and stir shallot and garlic in the hot oil until fragrant, 2 to 3 minutes. Stir in spinach and carrot mixture, chicken stock, white beans, oregano, thyme, salt, and pepper. Bring to a boil, stirring occasionally. Reduce heat and simmer until flavors combine, about 20 minutes.
Remove soup from heat and stir in lemon juice. Puree with an immersion blender until smooth.