Lightly oil the grates of your grill then preheat your grill on high heat with the lid closed until hot, about 15 minutes.
Cut your eggplant into about 3/4" slices and arrange in a single layer on a baking sheet or another surface. Whisk together the remaining ingredients (lemon juice, oregano, salt, pepper, and garlic) in a small bowl.
When ready to grill, brush the marinade onto both sides of each eggplant slice, making sure to get fresh garlic on the surface. Avoid brushing on the marinade much before you're ready to grill to prevent soggy eggplant.
Using long tongs, carefully place the eggplant in a single layer on the grill surface. Do not overcrowd. Do not close the grill.
Cook for 3 minutes without touching, then carefully lift up one slice of eggplant. If the underside is cooked with clear grill marks, flip all slices. If you want stronger grill marks and the bottom is not yet softened, continue cooking for another 2-3 minutes without moving, then flip all.
Cook for 3-4 minutes on the second side, until just tender when pierced with a fork. Do not overcook or the eggplant will become soggy. Immediately remove from the grill and serve.