Try using naan instead of pitas for an even more smokier flavor.
Prepare an ice-water bath. Cook green beans in a pot of boiling salted water until bright green and just tender, about 4 minutes. Drain; transfer to ice-water bath, and drain again. Cut into thirds. Toss with mint, cucumber, and lettuce.
Pour 1/4 cup oil into lemon juice in a slow, steady stream, whisking until emulsified. Season with salt and pepper.
Toast pitas over the flame of a gas burner, turning with tongs, until crisp and blackened in spots. (Alternatively, char in broiler, turning.) Rub with garlic, and brush with remaining 1/4 cup oil. Season with salt. Tear into large pieces. Drizzle dressing over salad; toss to coat. Serve with pitas.