I have never seen an Atari Lynx outside of a Sears Wishbook. Nintendo? Obviously. Sega? Equally so. The Turbographix 16 was even well-regarded at the time, and when the Atari Jaguar came out it was generally regarded as too little too late and wasn't that a shame because the graphics were pretty dope. But I don't recall any awareness whatsoever around the Lynx.
Yeah, the fact that I've had hands on experience (thanks to a network of friends who everyone owned something) with pretty much every system from that era except the Lynx, kind of says it must not have been too common. Poor battery aside, I can kind of see why. The games look colorful, but from some videos I've seen the frame rates look really chopy and the graphics look more on par with what you'd find on an Amiga or DOS computer, which back then, such graphics look really out of place on a console, even a handheld one.