Yes it does....a two year old MUST be held on a parents lap.
A two-year-old MAY be held on a parent's lap, there is no restriction anywhere, in fact, it is encouraged, that they ride in a safety seat to take advantage of safety belts. When we flew, up to 2-years-old could ride in the lap without paying for a ticket. We bought a ticket to accommodate a safety seat, as our just-under-two-year-old was too big (tall) to hold comfortably on a cross-country flight.
Here is Delta's guideline on that. http://www.delta.com/content/www/en_US/traveling-with-us/special-travel-needs/children.html
If the child is under two, he or she may sit in your lap, but there is no restriction against buying a ticket, or using a ticketed seat for a child under two.
ABSOLUTELY UNTRUE!!!!
Ticket Required You'll need to purchase a ticket for your child when you:
have a child that is age two or older.
have a child that turns age two during a trip — a reserved seat and ticket are required for the entire journey.
prefer the child to sit in a seat with an approved restraint.
Delta GUIDELINES FOR KIDS