I found the following on Peter Lorre's Wikipedia page:

An episode of the 50's television classic "The Honeymooners" features Jackie Gleason as Ralph Kramden threatening his wife Alice that if she doesn't comply with one of his demands he will "do his Peter Lorre imitation", apparently something Alice detests. When Alice does not immediately comply, Ralph launches into a bug-eyed caricature of Lorre, saying "Did you get the information, Mrs. Miller???" upon which Alice cannot stand it any longer and gives in.
Does anybody remember this scene? For some reason I don't, and I've seen every episode from the 50's that's "out there." Granted, Wikipedia is the source of this information, but I figured I'd post this in case anybody does remember seeing this. I remember Jackie doing a Peter Lorre imitation on his variety show, but it wasn't part of a Honeymooners sketch.

I don't remember watching that scene but it does sound like something Ralph Kramden would do.

I think I know. The episode was a Color episode entitled "The Match Game." Ralph & Alice are arguing. Alice is in the bedroom and she won't come out. Ralph demands her to come out or he will do his Peter Lorre impression. She doesn't so Ralph does his impression.

I think I know. The episode was a Color episode entitled "The Match Game." Ralph & Alice are arguing. Alice is in the bedroom and she won't come out. Ralph demands her to come out or he will do his Peter Lorre impression. She doesn't so Ralph does his impression.
I figured it was probably one of the color shows, thanks for clearing that up. It's interesting to note that Peter Lorre did his own Gleason imitation in a Honeymooners parody on The Red Skelton Show in 1955.

Is Peter Lorre who Gleason imitates in the "Three For Two" special that he did with Lucille Ball? It's in the first act, I believe, when the bellboy comes up into the hotel room.