Heat the oil in a large pot over medium heat. Add the onion, carrots and celery with a pinch of salt and cook until softened, 8–10 minutes. Add the garlic and cook 1 minute.
Add the split peas, broth, bay leaves, thyme, smoked paprika and potato. Bring to a boil, skimming off any foam.
Reduce the heat to low, partly cover and simmer for 60–75 minutes, stirring every 15 minutes and scraping the bottom, until the peas have broken down and the soup is thick.
Remove the bay leaves and thyme stems. For a smoother soup, blend part or all of it with an immersion blender.
Stir in the lemon juice and season generously with salt and pepper.
Serve hot with crusty bread.