Q. Back to lay/lie, which is my most unfavorite error! There is an exception to the answer you gave in a recent Q&A—“lay takes an object” EXCEPT when you’re talking about chickens! The hens are laying. (Of course, eggs are implied, but not mentioned.)
A. In grammar as in life, there will always be exceptions. Merriam-Webster does list a few intransitive senses for “lay,” the first of which is “to produce and deposit eggs.” But as you suggest, one person’s intransitive verb is another’s elliptical construction. You can call your cousins or just call [them]. And if you’re not laying eggs, what exactly is your object? (Please don’t lay into us on that one—yet another intransitive use for “lay,” in which the object requires the intervention of a preposition.)