Pat the 2 skinless, boneless chicken breasts dry with paper towels. Heat a thin layer of oil in a skillet over medium-high heat until shimmering.
Pan-fry the chicken breasts until cooked through, about 5–8 minutes per side depending on thickness, or until an instant-read thermometer inserted into the thickest part reads 165°F (74°C). Transfer the chicken to a cutting board and let rest 5 minutes.
While the chicken rests, combine 4 tablespoons soy sauce, 1 tablespoon lemon juice, 2 tablespoons sugar, and the 3 peeled ginger slices in a small saucepan.
Heat the saucepan over medium heat, stirring occasionally, until the sugar dissolves and the sauce slightly thickens, about 3–5 minutes. Remove and discard the ginger slices.
Slice the rested chicken into pieces, arrange on a serving plate, drizzle the warm sauce over the chicken, and garnish with the chopped scallion. Serve immediately.