In a small bowl, whisk together the lemon juice, tahini, water, and crushed red pepper. Add the extra-virgin olive oil 1 tablespoon at a time and whisk well after each addition. Set aside.
Preheat the grill to medium-high heat. Lightly brush both sides of the eggplant rounds with the avocado oil. Grill the eggplant for about 5 minutes per side, until grill marks develop and the eggplant softens.
Arrange the eggplant on a serving platter. Drizzle the tahini sauce over the slices. Scatter the scallions and cilantro across the eggplant, then sprinkle with cumin seeds. Serve warm.