Bring the coconut milk and water to just under a simmer with the ginger, lemongrass, and lime juice. Heat for a few minutes while you slice up the chicken breast. (It's easiest to slice meat thinly when it's partially frozen. I used a breast from the freezer last night so just thawed it partially.)
Add the chicken slices and cook until done, about 10 minutes. Add the lime juice, lemon juice, fish sauce, and sugar and heat through. Taste and adjust. (If I'd had lime leaves, they would have been added with the ginger and lemongrass at the beginning.)