When the vault dwellers are having a meeting on how to deal with the prisoners, they are interrupted by another dweller who claims that their water chip has been destroyed. This is a reference to the main plot device of Fallout (1997), where the main protagonist is tasked by his own vault, Vault 13, with exploring the wasteland to find a replacement for their water chip, which had broken.
"Maybe" by the Ink Spots, which plays when Lucy is first seen in this episode, was the music used in the memorable intro to the very first Fallout game.
The image of a lone Wanderer walking through the Wasteland with a dog is taken directly from the games, where a regular companion of the Vault Dweller is a very similar looking dog, usually called "Dogmeat", although in this case accompanying a ghoul rather than the Vault Dweller.
When the Gulper takes Lucy's yellow bag and is seen swimming away with it at the surface, this appears to be an homage to Jaws when the yellow barrel was attached to him showing his location in the water.
Gulpers first made another appearance in Fallout 4: Far Harbor and Fallout 76, where they appeared to be mutated hellbender salamanders. While they share a name and aggressive behavior with their video game counterparts, this iteration of the gulper appears to be a mutated axolotl (another type of salamander).