In a small jar, combine lemon zest, lemon juice, ginger syrup, shoyu, chili sauce, ginger, garlic, 2 T. vegetable oil, and salt.
Cover tightly and shake vigorously; refrigerate.
In a large skillet or wok, heat 1 c. vegetable oil over moderate heat until it just begins to smoke.
Cook the wonton strips in several batches until light golden brown, about 1 min per batch.
Drain wonton strips on paper towels.
Gently poach chicken until tender.
Cool and slice chicken into thin slices; set aside.
Stack the romaine leaves and roll up from the long side into a tight cylinder.
Slice the lettuce roll at ⅛" intervals.
Transfer the lettuce to a large salad bowl.
Add the carrots, green onions, and chicken.
Shake the dressing, pour it over the salad and toss.
At the last minute, gently sprinkle the wonton strips on top of the salad; serve immediately.