Mr CGV,
Very interesting question, and I thank you for posting it. You asked for comparisons between HK LEM and Glock triggers so here are my thoughts.
I own a G21 and a G30, and my wife owns a G26. The G21 and G30 have been worked on by TRGraham, a Glocksmith well known in the Texas parts. Both have 3.5 pound connectors and have super slick/smooth triggers. The 26 has the standard 5.5 pound connector but it's also been smoothed over by TR.
I also own an HK Compact .45 and my own copy of my duty weapon which is an HK Compact .40; all have the LEM trigger modules. The duty weapon (and my own exact copy) have the standard 8 pound LEM trigger. Actually, the trigger is technically listed as "7.5 - 8.5 pounds" but it comes out around 8. The Compact .45 also has the LEM trigger but with a 6.5 pound pull, and that trigger action has been smoothed by Tommy Thacker of Thacker Guns.
I like all of the above weapons, and all have advantages and disadvantages. The Glocks are dirt simple to maintain and are very accurate. The quality is very good and I would not hesitate to depend on them. As you know, the safety is in the trigger on the Glocks and after a while it begins to hurt my trigger finger. I have changed out the triggers to the smooth trigger and that does help a little, but not much. I find the Glocks, even after TRGraham did his magic, feel just a little "spongy." That's not a bad thing; it's just indigenious to the Glock trigger. The Glock reset is very definite and crisp.
The biggest downside of the Glocks is their size. The G21 is huge (and HEAVY when carrying high cap mags!), and the G30 is fat. It is about a quarter inch fatter than the HK, and believe it or not when carrying concealed it does indeed make a difference. Well, it does to me, anyway, and it also makes a difference to several of my carrying friends. The HKs just seem to feel better in the hand, but that's purely subjective. If the girth of the Glocks is not an issue for you, then that's terrific.
The HK is an extremely high quality weapon with many more parts than the Glock. This makes detail stripping problematic to say the least, and in fact detail stripping your HK will void your warrantee. Field stripping and cleaning on the HK, like the Glock, is very easy. There are detail stripping instructions available online for the standard SA/DA trigger but I've not seen detail stripping instructions for the LEM and I wouldn't dream of going beyond field stripping and cleaning without an HK armorer sitting next to me.
The LEM is an unusual trigger. It, like the Glock, is very consistent. It's the same trigger pull, all day, every day. As mentioned by others, it does have a long initial take-up which has little or any pull weight, and the LEM has a slightly longer reset. I do not find either to be problematic but again, this is purely subjective. I do not like my duty weapon's trigger pull as it's just too damn heavy for my tastes. Unfortunately, the agency didn't seek my opinion on trigger pulls (go figure!) so I have learned to live with my disappointment!!
However, the trigger pull on my customized HK Compact .45 is great! Tommy did a great job and although the Lyman electronic consistently says 6.5 pounds it feels more like 5 pounds. One caveat about the Compact .45 with the LEM, and this applies ONLY to the Compact .45 with the LEM, but they are prone to light hammer strikes (and subsequent misfires) if the trigger pull is lightened below the stock 6.5 pound factory springs. Tommy initially tried to go with the 5 pound springs and they didn't work in this particular model so we returned to the factory 6.5 pound springs and the problem disappeared. The reset is also crisp, but not quite as crisp as the Glock reset. I can tell you from personal experience that double taps are absolutely no problem with the HK LEM trigger.
I really like my Glocks and wouldn't dream of selling any of them. But the G21 sits in my safe and the G30 is in the nightstand lockbox. I'm a 1911 guy and my primary carry is a Kimber ProCDP 1911 (soon to be a Custom build Commander sized Caspian) with a 4.5 pound trigger. Nothing beats a 1911 trigger. But when I'm not carrying the 1911 I'm carrying my HK Compact .45 with the LEM.
I hope this information helps.
Mike