Did the Germans make lamp shades from prisoners' skin?

They didn't, but it is said that they used their skin to make other pieces of furniture, such as couches and rugs.

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No. At the time of the early postwar trials of concentration camp guards some journalists said that a few of the guards had had lampshades made out of the skin of prisoners with erotic tattoos. The strange thing is that these allegations were made only about female guards - the implication being that they were demonically perverted. All this was entertaining stuff for some readers.

It seems to be a popular urban legend.