For most airlines a child has to be under the age of 2 years old to fly for free sitting on the parents lap.
You must bring proof of the child's age to the airport when boarding to prove that the child is under 2 years of age so that they will let the under 2 year old child fly free on your lap.
A child 2 years of age or older must have their own seat and their own plane ticket to fly on the airplane.