Lollipop hold is great for a round, known diameter bulleye at an exact known range but is an absolutely horrible sight hold for anything else. It's a crime that some folks train people to shoot this way. Point of impact is an arbitrary distance above the front sight, the distance being determined by the bullseye diameter.
I've never seen a primary source that HK is setup to "shoot the dot", the white dot on the front sight. They may be. (I don't consider M4Carbine dot Net to be a primary source.) If anyone has some time I guess we could search the .PDF version of the HK manual and see what's there.
My P2000SK (and all my HKs) shoot point of aim. Tip of the front sight (maybe the dot) is where the bullet will imapct.
My P2000SK trigger pull was so hard in standard LEM I was shooting left too. Reduced the pull to about 5.5 pounds and she's dead on. Years of 4.5 pound M1911s didn't help my trigger control with hard pulls.