Place 1 cup split red lentils and 3 cups water or stock in a 3-quart saucepan. Bring to a boil over high heat, then reduce heat to low, cover, and simmer until lentils are tender, 5–7 minutes. Drain the lentils in a fine-mesh sieve and set aside to cool to warm or room temperature.
While the lentils cook, preheat the oven to 475°F. Place 6–8 garlic cloves on a piece of aluminum foil, drizzle with some of the 3–4 tablespoons olive oil listed, wrap the foil to enclose the garlic, and set the packet on a baking sheet.
Roast the garlic packet in the preheated oven for 15–20 minutes, until the garlic is fragrant and softened. Remove from the oven, unwrap carefully (steam will be hot), let cool slightly, then peel or squeeze the roasted garlic cloves out of their skins.
Add the drained lentils, the roasted garlic cloves, the juice of 1 lemon, ¼ cup Italian parsley (chopped if desired), 1 teaspoon salt, and ¼ teaspoon pepper to a food processor. Process until mostly smooth.
With the food processor running, drizzle in the remaining olive oil from the 3–4 tablespoons listed until the dip reaches a smooth, silky consistency. Stop and scrape down the sides if needed. Taste and adjust salt and pepper if desired.
Transfer the dip to a serving bowl. Garnish with a sprinkle of parsley and a drizzle of olive oil if you like. Serve with pita chips, crackers, or vegetables.