For the eggplant:

1 1/2 pounds eggplant (about 2 small)
2 teaspoons kosher salt, plus more as needed
4 tablespoons extra-virgin olive oil
Freshly ground black pepper
1 teaspoon finely chopped fresh Italian parsley leaves
1/2 teaspoon red wine vinegar
Pinch red pepper flakes
For the sauce:

2 (28-ounce) cans whole peeled tomatoes, preferably San Marzano
1/4 cup extra-virgin olive oil
1 medium yellow onion, finely chopped
2 medium garlic cloves, minced
1 tablespoon tomato paste
1 bay leaf
1/4 teaspoon red pepper flakes, plus more as needed
Kosher salt
2 tablespoons capers
For the noodles:

Kosher salt
12 ounces dried lasagna noodles
For the filling:

2 pounds soft tofu, drained
1/3 cup finely chopped Italian parsley leaves
3 tablespoons nutritional yeast (optional)
2 teaspoons finely grated lemon zest (from about 2 medium lemons)
2 tablespoons freshly squeezed lemon juice, plus more as needed (from about 1/2 lemon)
2 teaspoons kosher salt, plus more as needed
1/2 teaspoon freshly ground black pepper, plus more as needed
To assemble:

1 cup loosely packed basil leaves (from about 1 bunch), cut into 1/4-inch-thick ribbons