I've only ever owned an HK45 in the DA/SA configuration but I have owned it's little brother, the P30L, in both DA/SA (v3) and LEM trigger (v1), so my comments will be based on that, but I can't see the HK45 being much different. Plus, my experiences with these triggers seems to mirror what I have read elsewhere.
After the first shot, you would be very hard pressed to notice any difference at all between an LEM trigger and the SA trigger, as long as you are working the reset of the trigger an not letting the trigger out fully between each shot. If you do let the trigger out you will experience a quite longish but light take up before the trigger breaks. It does not feel like double action, but it doesn't feel quite like single. You have to shoot a LEM to fully get how it feels, but it is decent.
When it comes to the first shot, the DA pull of the DA?SA gun feels nothing at all like the LEM. The HK DA pull is nothing short of awful. Stupidly heavy and annoyingly long. By far the ugliest DA pull of any modern handgun - bar none.
In contrast, the first shot from the LEM trigger feels just like any other shot from the LEM trigger. light but longish take up and a clean light break with a bit more overtravel than I'd like to see, followed by a crisp but longish reset.
The real advantage of the LEM is that, much like striker fired Glocks and M&P's, there is a consistent feel between the first shot and every other short fired; but in a hammer fired pistol. I really like the LEM for that very reason.
If HK ever decides to shorten the reset of that trigger, I will definitely buy another P30 series gun. I love everything about that gun except the too-long reset.