Lawessons reagent has a four membered ring of alternating sulfur and phosphorus atoms.  The central phosphorus/sulfur four-membered ring dissociates to form two reactive dithiophosphine ylides (R-PS).  Much of the chemistry of Lawessonss reagent is in fact the chemistry of this reactive intermediate.
In general, the more electron rich a carbonyl is, the faster the carbonyl group will be converted into the corresponding thiocarbonyl by Lawesson's reagent.