Your LNL AP will resize .223 just fine if you lube the cases as you should, it has as much or more leverage than most all of the single stage presses. I've resized many thousands of .223s in mine. The trick is getting a good lube.
I used to use the Hornady one-shot, worked so so and expensive. I'm finishing up 5K of .223 as a winter project and these days I use some carnuba wax, just rub a little on my left hand and hold the cases in that hand, pull the lever with my right, works much better than the hornady spray lube and I've used maybe 50 cents worth of the wax in 5000 cases.
One thing, if it feels like the case sticking on the downstroke, go REAL slow and often it will ease out instead of yanking the rim off.