Let's see.
Argonians are ovoviviparous. [Wow. I was SURE I'd never have to use that word again.] They don't lay eggs like reptiles.
Note that Lady Argonians have big bumps on their chests.
Men and Mer assume much about Argonians, but who among them has ventured deep into Black Marsh and lived to tell about it? They assume that Argonians lay eggs because they resemble the tree-dwelling lizards that scurry about on four legs. Yet they assume Argonians have live births, because the females have briasts with which they might svckle their young. Perhaps it is both, as necessity demands. All live at the whim of the Great Root.
Never underestimate the adaptability of Argonians, or, more specifically, the power of the Hist to allow Argonians to adapt.
I wouldn't expect to hear an Argonian born in Skyrim (or on Solstheim, for that matter) mention being hatched. Nor would I expect to hear more transient Argonians (say, members of a small, nomadic tribe) speak about laying eggs. However, in warmer climates, in places with established, stable, and permanent communities, you would likely see a great number of eggs.