Palm reading, or Palmistry, is viewed as a pseudoscience by academics, due to the contradictions between different interpretations of various lines and palmar features, as well as the lack of evidence of predictions.
Lily gives her age as 137, which means she was born in 1827.
Grandpa tells Herman that Lily goes out wearing her most exotic perfume, 'Chanel No. 13'. There are several theories as to why the number 13 became associated with bad luck (and probably why the Munsters enjoy it). For example, a year with 13 full moons instead of 12 posed problems for monks in charge of calendars because it would upset the regular arrangement of church festivals.
When Marilyn answers the phone she tells Lilly that her Cousin Lester is on the phone when earlier in the show it was told that Lester was Grandpa's son which would make him Lilly's brother.