Except in the Pacific Northwest, trails rarely are covered entirely in shade, so your child will need protection from the sun for both skin and lips.
For sunscreen, use a low scent/no scent variety. Scents can attract insects (leading to other issues) and even bears (really leading to other issues).
Use a children's sunscreen rather than one for adults, as some kids' skin can be sensitive. Look for sunscreen free of para-aminobenzoic acid, or PABA, as the chemical may cause skin problems for children.
An SPF of 30 is good.
For lip balm, make sure it has a SPF in it or lips will burn.
Read more about day hiking with children in the guidebook Hikes with Tykes.