I have no idea where the term originated, but a Lemming polish is simply a polish you very desperately want to get your hands on. It's one at the top of your wishlist and you will probably spend more money that you should to get it. I have a handful of lemmings myself, one of which I just got a dupe of and am thrilled even if it's not exactly the same thing.
I've never bough Salon Perfect before, but when they released this polish I spazzed out a little bit. It is nearly an exact copy of Ninja Polish "Floam", one of my lemmings.
China Glaze "Whirled Away" was another attempt at fulfilling a lemming desire. Again I so want Ninja Polish "Sticks and Stones" but it is usually sold out so I got this to try and replace it. It is not nearly as close a dupe but it will do till I find something better.
Some of my other lemmings:
Color Club Halo Hues
China Glaze OMG Collection
Finger Paints Special Effects Collection
Almost anything by Nerd Lacquer but especially "Don't Blink", "I Think You Call Me...Sexy", "Don't Panic" and "Gorramit".