Was there an episode that showed Frasier and Lilith actually getting married or did they just tell everyone that they got married.

They just told them that they got married.

Frasier proposes to Lilith at the end of Episode 126 "The Crane Mutiny" which is the 5th episode in the Rebecca Years. And from there on out it is assumed that they are married.

There was no wedding episode which is kind of surprising because they could have done alot with that. But they probably thought that since the 2 episodes previous to that were Carla and Eddie's wedding, that they would be doing weddings to death.

Frasier and Lilith do renew their wedding vows in Episode 239 "Smotherly Love"

I believe after the episode, "To All the Girls I've Loved Before" it was assumed they were married. That was the bachelor and bachelorette party episode, and Frasier says something along the lines of, "I still want to marry you anyway." And Lilith replies in a drunken stupor, "Frasier, I will always cherish those words. 'Lilith, I still want to marry you anyway.'" LOL Afterwards, they were just regarded as husband and wife if my memory suites me. Hmmm.