Measure and look through lentils and barley to remove any rocks or debris that might be mixed in. Add to a large bowl, cover with 1 to 2 inches of water. Soak for 30 to 40 minutes, while you prep the rest of the ingredients and begin cooking the soup. This will help to remove excess starch and reduce cooking time.
Pour oil into a large pot over medium heat. Add onions and cook for 3 to 4 minutes, stirring intermittently. Stir in garlic and cook for 1 more minute.
Add diced carrots, celery, tomato paste, oregano, cumin, coriander, paprika, salt, and pepper. Stir to combine. Cook for 3 to 4 minutes.
In a colander, drain and rinse lentils and barley. Add them to the pot.
Pour in 7 cups of broth. Bring the soup to a boil, then reduce the heat to low and simmer, covered, for about 25 minutes. Stir halfway through cooking.
After 25 minutes, add spinach, parsley, and lemon juice. Stir again to combine. Cook for 10 to 15 additional minutes.
Taste and add more salt and pepper, if desired. The soup is meant to be thicker as the lentils and barley will absorb liquid, but you can add up to an additional 1 cup of broth depending on your desired consistency.