LEM stands for Law Enforcement Modification and is a form of DAO. No external safety.

Yeah, with the LEM trigger it's like a DA revolver. There's no decocker or safety. When you rack a round into the chamber it takes a long but not especially heavy pull to fire the gun. With HK, the reset on subsequent shots is much shorter. So when I hear folks bust on the LEM trigger I wonder if they are controlling the trigger such that they only release it to the reset point for all shots after the first. I have the P2000 with the LEM trigger and like it very much,.

Sig makes a similar DA trigger setup they call DAK.

The USPc I just got has the V1 DA/SA. It has a safety which is also a decocker. So you can chamber a round and decock the hammer and carry the gun so that it takes a long, hard DA pull to fire. Or you can carry it in "condition 1" like a 1911, cocked and locked, i.e., with a round chambered, the hammer cocked and the safety on. To fire, drop the safety and a light short pull fires the gun.

Hope this helps.

So LEM is a version of DAO ? I need more info.

I would like more detailed information on these trigger options. Not just symptoms.

You might try HKpro forum. they have folks there that really know HK firearms. I'm not sure what info you want. Beyond describing what the acronym stands for and how it operates, I'm at a loss.

HK has the manual online.

http://www.hk-usa.com/images/shared/compact_lem_man.pdf

Basically when you rack the slide, the internal hammer is pre-cocked.
There is a long, light trigger pull and then a medium effort to fire.

With the trigger held back, The slide movement cocks the hammer again.
With a very short trigger reset, the trigger can be pulled again with a light effort to fire.

If the trigger is more fully released, the gun is back to the earlier pre-cocked state.

I am still getting used to it. What I like about it is that as a left hander I don't have to worry about it being variant 1 or 2 or ambi. It basically "de-cocks" by fully releasing the trigger.

Hope this helps.