I dunno many songs with three part harmonies, however you can acapella almost any song anyway. So I'll just list songs that would be fitting to someone who is retiring.
My Way - Frank Sinatra:
The Best Is Yet to Come - Frank Sinatra:
As time goes by - Lous Armstrong:
(if your grandmother has a sense of humor about the situation)
Take this job and shove it - Johnny Paycheck:
(and if you want to be really cheesy, proper cheddar man)
I’ve Had the Time of My Life - Bill Medley and Jennifer Warnes: