I think the colloquial usage has roots in Python's use of it, I've been hearing about anonymous functions being called lambdas for a long time. The Lambda service's name seems to play on that prior colloquial usage.
https://sarabander.github.io/sicp/html/1_002e3.xhtml#g_t1_00...
https://archive.org/details/recursive-functions-symbolic-exp...
My hot take for which I'm sure I'll get some hate is all languages should just include js-style arrow functions
Honestly it's likely that for most of the history of the term it's been more used for "incorrect" meanings than "correct" ones.