Preheat oven to 450 degrees F; prick eggplant all over and roast in a small baking dish until very tender (it will collapse), about 40 minutes (turn once or twice).
Meanwhile, in a large saucepan, heat 2 tablespoons of the oil until it shimmers; add cumin seeds and crushed red pepper and toast, while stirring (to prevent burning), until fragrant, 1 minute; add garlic and cook 30 seconds.
Stir in the lentils and water; season with salt and bring to a boil. Cover, reduce heat, and simmer and cook until lentils are just tender, but not mushy, about 40 minutes; transfer to a serving bowl.
Scoop the flesh from the eggplant and chop it; allow chopped eggplant to drain through a fine sieve to remove excess liquid.
Add eggplant to serving bowl, along with lemon juice, mint, parsley, remaining 1/4 cup oil; season with salt and pepper and gently toss and stir to combine. Serve warm or room temperature with warm pide and plain yogurt.