Set up your frying station by lining a plate with paper towels. Tear the pita into irregular, bite-sized pieces — uneven shapes hold the dressing better. Heat 3 tbsp olive oil in a large skillet over medium heat until it shimmers. Add the pita pieces and fry, tossing constantly, until they're deeply golden and crispy. Transfer immediately to the paper towel-lined plate and season generously with salt, pepper, and sumac while they're still hot.
Toss the chopped lettuce, cucumber, tomatoes, green onions, radishes, parsley, and mint together in a large mixing bowl. The vegetables should be roughly the same size so every forkful has a good balance of flavors and textures.
Make the dressing by whisking together the lemon juice, olive oil, pomegranate molasses, salt, pepper, sumac, cinnamon, and allspice in a small bowl. Whisk vigorously until the mixture emulsifies and the spices are fully incorporated.
Pour the dressing over the vegetables and toss thoroughly to coat everything evenly. Add the warm, crispy pita pieces and give everything a final gentle toss — you want the pita to soften slightly but still maintain some crunch. Taste and add more sumac if you want extra tang, then serve immediately.