What are some examples of word-play in constructed languages such as Esperanto and Lojban?

Esperanto neurotically tried to avoid lexical ambiguity, but didn’t get there for compounding, and between that and soundalikes, it’s doing ok. Raymond Schwartz was the main punmaster of the language.

Examples: the sundry aĝo “age” compounds in La Diversaj Aĝoj de l’ Homo, or the groanworthy “tumble dry” of Molière in El “Verdkata Testamento” (1926); Ero (lava rulo; The Miser is L’avarulo).

Lojban really is designed to avoid lexical ambiguity, including at compounding, and I don’t remember much play there, if any.

Klingon has a fair bit of polysemy, and that has been used for jokes. I’ve mentioned here, I think, my spontaneous pun when I walked into my first Klingon meetup, and a guy I’d managed to antagonise said SaH ’Iv? (“Who cares?”) Quick as a pistol, I responded jISaH jIH, naDev jIHmo’: “*I*’m present, because I’m here.” (The verb is ambiguous.)

Polysemy also explains a joke by Okrand, which at first glance seems to be an anti-joke:

Doq’a’ SuvwI’pu’? ghobe’! SuD! “Are warriors red? No! They are blue!”

The chuckle by Michael Dorn on the recording was… unnerving.

But SuD doesn’t just mean blue. (Or green. Or, in violation of how human colour works, yellow.) SuD also means “to take a risk”…