Rinse both types of lentils under cold water and pick out any debris; drain well and set aside.
Warm the olive oil in a large Dutch oven over medium heat. Add the chopped onion, carrots, and celery and cook, stirring occasionally, until softened and translucent, about 6–8 minutes.
Stir in the minced garlic, ground cumin, and smoked paprika and cook for 30–45 seconds until fragrant. Pour in the canned tomatoes (with their juices) and scrape up any browned bits from the bottom of the pot.
Add the rinsed lentils and vegetable broth. Increase heat to bring the mixture to a gentle boil, then reduce to a simmer. Partially cover and simmer until the lentils are tender, about 25–30 minutes for this mix of brown and red lentils.
For a thicker, creamier body, use an immersion blender to pulse about one-third of the soup right in the pot (or transfer one-third to a blender and purée), then return it. This keeps texture while naturally thickening the broth.
Stir in the chopped spinach and lemon juice and simmer 2 more minutes until the greens have just wilted. Taste and adjust seasoning with more salt or pepper if needed. Remove from heat and let the soup rest uncovered for 5 minutes so flavors meld.
Serve hot in bowls with a dollop of Greek yogurt and a sprinkle of chopped parsley. Leftovers keep well and often taste even better the next day.