She responds that the only thing she will inherit is a valuable silver tea and coffee service, an heirloom which has been in Edith's family for 100 years.
It is then that Veronica reveals that she and Liz were more than just friends, colleagues, and roommates: they had been in a committed lesbian relationship for the past 25 years.
Archie hits the roof and demands that Veronica return the tea service, and when she refuses, he threatens to sue her, which would expose her relationship with Liz and possibly cause her to lose her job.
[1][2] The episode was cited by The Christian Science Monitor as being "compassionate" and Veronica's coming out to Edith as "one of the most delicately handled sequences of the entire series".
[3] "Cousin Liz" aired at a time when Anita Bryant and her Save Our Children coalition were sponsoring a series of ballot initiatives to repeal gay anti-discrimination ordinances across the country.