First, to explain why the "joke" is "funny" (inverted commas because I don't find it funny, and I suspect many others don't either). Thanks to Flater and knzhou for explaining this.

During the time of manually-operated elevators, there were so-called "[elevator operators][1]" who would ask passengers where they were going. A possible answer for example could be "second floor". In those days, departmental stores were also organized by departments that could take up an entire floor. To say "take me to the ladies' lingerie department" is equivalent to saying "take me to whichever floor sells ladies' lingerie". The joke is that the speaker, as a man, is not expected to want to buy ladies' lingerie. The same joke would work with a female speaker asking to be brought to the men's lingerie department.

The joke is offensive because the listener didn't understand it. Since some people laughed, the listener knows it's a joke. However she didn't know why it's funny - not surprising, from the comments many don't either. Still, **since 1) women and 2) lingerie were mentioned, she assumes that it's a sexual joke**. That immediately makes it offensive.

Here're a couple of other situations which were interpreted badly: [when a man invited a woman to coffee in an elevator][2], and a [joke about dongles and forking at a technology conference][3]. You can easily find more using Google for terms such as "humor in different cultures".

As to the question of how to avoid it: **unless among friends, avoid making jokes entirely because humor translates poorly across cultures.** This is the same reason that one should avoid injecting humor into e.g. a conference presentation. As you can probably imagine, the hassle that Prof. X is going through is not worth the laughs he got.


  [1]: https://en.wikipedia.org/wiki/Elevator_operator
  [2]: https://en.wikipedia.org/wiki/Rebecca_Watson#Elevator_incident
  [3]: https://en.wikipedia.org/wiki/Online_shaming#Adria_Richards_incident