The LEM Models are double action only, whereas teh P30sk is single/double. The LEMs have The HK Law Enforcement Modification trigger system which combines the advantages of a cocked striker component (constant level of trigger pull from first to last round fired) with a double-action hammer system.
Developed especially for a U.S. government agency, the Law Enforcement Modification (or LEM for short), is a unique trigger mechanism created specifically to improve the trigger performance and reduce the weight of the Double-Action Only (DAO) trigger pull on HK pistols.
With this mechanism, HK pistols can be fired like a standard DAO semi-automatic pistol where every round is fired by simply pulling the trigger fully rearward with the hammer starting at the forward rest position. The design of the proprietary HK LEM system allows the weight of the DAO trigger pull to be reduced to a smooth and constant 6.18 - 8.5 pounds (27.5 - 37.8 N) because the two-part hammer is pre-cocked every time the slide moves rearward. Trigger pull on conventional double action pistols is 12 - 15 pounds (53.4 - 66.7N).

The LEM is enhanced DA trigger only the p30sk is a DA/SA trigger I like DA/SA firearms as it is what I know and shoot

The LEM model, has double action capability, the only external controls are an extended slide stop and a paddle-style magazine release. These controls are mirrored on both sides — fully ambidextrous. The P30sk with the ext safety has the "Standard Trigger" and Manual Safety as the only differences compared to the LEM model.