She sang on the last episode
Lesley Gore (May 2, 1946 – February 16, 2015).
Lesley Sue Goldstein, known professionally as Lesley Gore, was an American singer, songwriter, actress, and activist. At the age of 16, she recorded the pop hit "It's My Party" (1963) which topped the charts and followed it up with other hits, including You Don't Own Me and seven further Billboard top 40 hits.
She appears in the last episode of The Donna Reed Show in “By Line – Jeffrey Stone” (Season 8, Episode 27) singing "It's My Party."