Break pita into small pieces and fry in 3 tablespoons olive oil over medium heat until golden and crisp, tossing frequently.
Transfer crispy pita to a paper-towel-lined plate and season with salt, pepper, and sumac.
Combine lettuce, cucumber, tomatoes, green onions, radishes, parsley, and mint in a large bowl.
Whisk together lemon juice, 1/3 cup olive oil, pomegranate molasses (if using), salt, pepper, sumac, cinnamon, and allspice.
Pour dressing over vegetables and toss gently to coat.
Add crispy pita just before serving, toss once more, and adjust seasoning with additional sumac if desired.