Frontier Airlines allows infants from seven days old up to the child’s second birthday to fly free of charge in an adult’s lap. They must be added to your reservation and will have a boarding pass, even if they don't occupy a seat. A maximum of 1 Infant on Lap per adult is allowed, otherwise an extra seat will need to be purchased for your baby to sit in.
A lap infant does not have their own assigned seat, meaning that they will be on your lap for the duration of your flight, and may not use a car seat in flight.
Note: If you prefer that your baby fly in a car seat, you may purchase a regular ticket for your baby and they will get their own assigned seat on which you can install your child's car seat. Keep in mind that the car seat must meet FAA's safety requirements for use on an aircraft, and must meet the labeling requirements that say so. Look for a label that says "This restraint has been certified for use in motor vehicles and aircraft" in red lettering.