If using dried coconut, soak it in 1 cup of boiling water until softened, about 15 minutes. Then, drain the coconut, reserving the water.
Transfer the coconut, ginger, garlic, serrano, and ¼ teaspoon salt to a blender and process until combined. Add the cilantro, mint, and lemon juice and blend until smooth. Then, gradually add water or the coconut steeping water as needed to smooth out the sauce and reach desired consistency (it should be thick but spoonable). Season to taste with pepper and additional salt. Store chutney in the refrigerator for up to three days.