Combine vinegar, sugar, salt, and water in a small saucepan and bring to a gentle simmer over medium heat. Place the onions in a heatproof bowl and carefully pour in the hot liquid, pressing down with a spoon to submerge. Cool to room temperature.
Heat the oil in a small skillet over medium heat and fry the pita strips until crispy, tossing occasionally. Spread onto a paper towel-lined plate.
Mix the crumbled feta and dill in a small bowl.
In a large mixing bowl, toss together the pickled onions, lettuce, cucumber, roasted tomatoes, chickpeas, and olives.
Blend all the dressing ingredients together, adjust seasoning to taste, and drizzle over the salad. Toss to combine.
Divide salad between 4 serving bowls and scatter dill feta and pita chips on top.