Actually, infants/children can sit on your lap regardless of age.

The 2-year-old policy is for ticketing purposes. "Commencement of the journey" is a bit vague but I interpret it as "the first leg of PNR".
Children can sit on your lap for takeoff/landing so long as they are under 15kgs. This restriction is to do with safety and the parent being able to cope with extra weight during an emergency.