From your question it is not clear whether there is only injury on the lips or also it is there for the teeth as well.if the tear on the lips are small like 1 or 2 cm and not much deep,that is less than 1 cm,it will get healed by itself,you don't have to worry.
Next Steps
I suggest getting a dental consultation in case your child is having pain
Health Tips
ice pack will help in reducing pain and swelling