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In the opening cutscene to Stage 1, the excuse Lammy comes up with while running backstage is an exact description of the setup to the Stage 5 song "Full Tank" from PaRappa the Rapper, ending on a cameo by the teachers from that game and reusing voice clips of them saying "Let's rap for it!!" from Full Tank's opening cutscene:

Lammy: "What should I tell them?? I had a stomachache so I went to the bathroom......but there was a long line at the gas station......I told them it was an emergency......but they said: "LET'S RAP FOR IT!!!". ... Nahhh...."
Contributed by MehDeletingLater
At the beginning of Stage 5, during the intro when Lammy is panicking, she will make a face similar to that of "The Scream", and art piece created by Edvard Munchs.
Contributed by DarkChojin
There are two versions of the 6th stage. In the Japanese and PAL versions of the game, the stage takes place in hell. In the American version, the stage instead takes place on a volcanic island. Both stages have different graphics for Lammy, a different intro cutscene, and a slight change in lyrics in the first stage to remove any references to hell or the devil.
Contributed by gamemaster1991