Bring a large pot of lightly salted water to a boil. Cook spaghetti at a boil until tender yet firm to the bite, about 12 minutes; drain.
Stir water, peanut butter, garlic, soy sauce, lemon juice, and ginger together in a bowl until smooth; set aside.
Heat peanut oil in a large skillet over medium-high heat. Fry tofu in oil until lightly browned, about 5 minutes. Add leeks; cook and stir until the leeks soften, 2 to 3 minutes. Stir Thai chilies into the tofu mixture; toss to combine and cook until the chilies are hot, about 1 minute.
Remove skillet from heat. Add spaghetti and peanut butter sauce to the tofu mixture; toss until everything is evenly coated in sauce. Season with chile-garlic sauce to serve.