I never understood the LEM trigger. I do know it was developed for the now defunct INS under the procurement contract for the HK USPc in .40 S&W. It was a damned fine carry gun at the time, and a vast improvement over the Beretta 96D (aka, the burrito) although I never cared for the overly long take up. As an instructor, I taught the other agents to shoot it like a two stage trigger, and that helped them immensely in getting used to the LEM trigger. The release and reset were very nice (considering what the gun was made for), and double taps were easy to do with it. After the merger and creation of ICE, I was thoroughly disappointed with the abomination that is now the Sig 229 DAK. That is one effed up gun. Heavy, impossible to conceal, terrible trigger, and a failure rate that almost surpasses the Beretta 96D.
For anyone out there who thinks the triggers on any of those guns is something desireable, I am sorry to disappoint you/ offend you by besmirching the triggers on these guns. The real reason the triggers exist is because it was specified in a .gov contract to make the muckety mucks feel better about the lowest common denominator of an armed officer carrying them. The goal was, afterall, to make the triggers as revolver like as possible because it was thought such a trigger is "safer". Good marketing ensured the time their R&D put into the trigger made them some extra money. Not unlike touting the NY trigger in the Glocks as something desireable because a well known LEA uses it. The LEM trigger was the best of the three though, and was even somewhat useable. The USPc in .40 was just a damned nice pistol and as accurate as they come in spite of the 3.5" barrel, high sight profile, and tolerable LEM trigger.
I sent over 35k rounds through 3 LEM equipped USPc's before I finally had to turn my last one in for the 229. Fortunately, I was able to buy a new LEM equipped USPc with 6 mags and night sights for the special INS officer price of $600. I later converted it to a DA/SA trigger and have been greatly pleased with it ever since.
ETA - I was fortunate enough to carry an HK P7M13 in my first LE job. Those guns are without a doubt the best engineered and most accurate service pistol I have encountered. The only thing I do not like about them is the heat generated from the gas retardation system. The plastic heat shield helps a little bit, but I still got burned by the SOB several times during long strings of fire in training. Way cool gun, and worth every penny when you can find one that has been cared for.