I'll repeat what I've said in other Lock-n-Load AP threads: Some Lee die sets won't work in a Lock-n-Load AP press. It's an issue of threading on the die body. Certain Lee die sets - maybe many of them - allow for insufficient adjustment, because of the height offset imposed by the Lock-n-Load bushing into which you must install the die, and because of the geometry of the L-n-L AP.
It's a bit difficult to envision this if you haven't tried it. The problem is chiefly with the size/deprime die. I tried to use a set of Lee .40 S&W/10mm pistol dies in my Lock-n-Load AP, and found that I could not adjust the size/deprime die far down enough. There simply wasn't enough threading on the die body. By the time I got it as low as I wanted it, no threads on the die were engaged with the lock ring. That meant the size die was not held solidly, but was free to rotate, giving inconsistent results and flopping around. Not good.
Note that all this may not apply to the Hornady Lock-n-Load *single stage* press. It probably has completely different geometry, compared to its progressive brother, and Lee dies may work there.