Preheat oven to 450 degrees F. Lightly brush eggplant with the vegetable oil, then pierce the skin with a fork several times, about 1 inch apart. Place on baking sheet and bake until eggplant is soft and the skin is dark brown and caved in, about 1 hour.
Cut about an inch off the eggplant at the stem and throw out. Peel the skin of the eggplant by picking at an edge from the cut side and pull up. Skin should come off in strips easily.
Cut the eggplant in half lengthwise, then spoon out the seeds leaving as much of the flesh as possible. Cut each half of the eggplant in half again and remove whatever seeds are remaining. Let eggplant sit a few minutes once you have removed the seeds to let excess water out.
Place the eggplant in a bowl, mash with a spoon first, then whip until it is smooth and soft. Using the coarse side of a grater, grate the onion right into the bowl. As you grate the onion, liquid will come out; let that go into the bowl it is needed for seasoning.
Add in the lemon juice, mix well with a spoon until thoroughly mixed. Continue stirring and add in the olive oil in a thin stream. Season to taste with salt and pepper if you choose.