Someone with an Army (SAMS?) background can better recount the development of the LOO concept, but it preceded the present conflicts and, I think, has its origins in the complex contingencies of the 1990s. In looking at older briefs and documents, there was a very rigorous and thoughtful way for planners to look at the problem and see if LOOs were necessary, and if so, what the LOOs should be. I think it had to do with complex problems not having single identifiable COGs, but possibly multiple COGs--each requiring actions along a seperate "Logical Line of Operation" (the conceptual equivalent of Jomini's physical line of operation--we dropped the "logical" piece to the title as no one remembers the physical origin and no one wants to associate our current COIN doctrine with a guy named Jomini). The commander had to arrange and coordinate all his actions across the LOOs to achieve his objective.
The Marine Corps never really embraced this doctrine until the early Irregular Warfare pubs--which to me looked largely like expansions of Chiarelli's article on LOOs in Baghdad in Military Review--a seminal piece, to my mind. From having no doctrinal background on LOOs, all of a sudden Marines were identifiying specific LOOs for COIN. Now LOOs pop up everywhere. The Marine Corps has still failed to grapple with them in any of our base doctrinal pub (the MCDPs). I look forward to that happening someday, because I think for LOOs to be useful, they can't be some template that commanders/planners just fill in the blank and start executing. Not every conflict porblem requires LOOs.
In many cases, even in complex scenarios like COIN, I see LOOs used as the equivalent of expanding the warfighting functions (maneuver, fires, logistics, etc.) into the "non-lethal" sphere. This tends to drive units to assign different parts of their forces to the various LOOs and they become almost separate commands at the higher echelons. I thought that the utility of the orginal way of thinking about LOOs was that it forced more synergy--a "kinetic action" was not relegated to a "combat action" LOO, but could affect multiple LOOs (information, enemy destruction, etc.). For the Marine Corps, its well worth looking hard at the LOO (and tell me, what is our 1-2 sentence definition of a generic LOO and what USMC or joint pub we use for it?).