In a small bowl, whisk together vinegar, lime juice, ginger, and sugar. Gradually whisk in oil, adding it in a slow, steady stream, and continue whisking until mixture is emulsified. Season with salt and pepper.
Place avocado in the center of a chilled serving plate. Season with salt and pepper. Beginning with the smallest lettuce leaves, add to dressing just to coat. Place dressed leaves around and over avocado. Repeat the dressing and layering process working from smallest to largest leaves. Sprinkle with sesame seeds and sea salt. Serve immediately.