Put eggplant cubes into colander and toss with 2 teaspoons salt and set aside. Bring a large pot of water to a boil.
In small bowl, mix hoisin sauce, water and lemon juice and set aside.
When water boils, add pasta and 2 teaspoons salt, stirring to prevent pasta from sticking. Cook, stirring occasionally, until pasta is al dente, about 10 minutes.
Meanwhile, in large nonstick skillet, heat sesame and vegetable oils over medium heat. Add garlic and cook, stirring often, until fragrant, about 30 seconds. Add eggplant in batches, squeezing out as much water as possible. Cook, stirring often, 5 minutes. Add hoisin mixture and stir well. Cover and cook, stirring occasionally, until eggplant is tender, about 10 minutes.
Drain pasta and transfer to large bowl. Add eggplant mixture and toss to mix. Season with salt and pepper.