The funeral in that episode (not the “non-denominational” service that Jed is referring to in the quoted dialogue) would have been an Episcopal service and used the order of service for The Burial of the Dead from the Book of Common Prayer. According to the rubric, the Lord’s Prayer is not said until The Committal, the actual placing of the casket in the ground. The part of the service that takes place in the church (the Collects, the Liturgy of the Word, the Eucharist (if used), and the Commendation). So at the point you’re leaving the church to go to the cemetery or columbarium or wherever the body will be placed at rest, you haven’t heard the Lord’s Prayer yet.