In a medium bowl, mix bulgur with 1/8 teaspoon salt and 1/2 cup boiling water. Cover; let sit until bulgur is tender (but still slightly chewy), about 30 minutes.
Meanwhile, in a small dry skillet over very low heat, toast pine nuts, tossing constantly, until golden, 3 to 4 minutes. In a small bowl, whisk together lemon juice and oil. Season with salt and pepper; set aside.
Drain bulgur in a fine-mesh sieve, pressing to remove excess liquid; return to bowl. Add feta, shallot, parsley, cucumber, and 1/2 the dressing; season with salt and pepper. In another bowl, toss lettuce with remaining dressing. Top with bulgur mixture and pine nuts.