In a medium bowl, toss the chicken with 1 tbsp. soy sauce, the cornstarch and half the garlic. Let marinate 10 minutes.
Meanwhile, in a large skillet or wok, heat 1 tbsp. oil over medium-high. Add the remaining garlic and cook, stirring, until fragrant, about 30 seconds. Add the asparagus and 1 tsp. water; season and cook, stirring, until crisp-tender, about 2 minutes. Transfer to a bowl.
In the same skillet, heat the remaining 2 tbsp. oil over medium-high. Add the chicken in a single layer. Cook, without stirring, until browned on the bottom, about 2 minutes, then cook, stirring, until cooked through, about 1 minute more. Stir in the lettuce; season and cook until just wilted, about 30 seconds. Stir in the asparagus and the remaining 1 tbsp. soy sauce. Season. Serve with the rice and garnish with the mint.