What Caused the Engine-Failure of Southwest Airlines Flight WN-3472?
The currently known details are that it was caused by the failure of a single fan blade, due to a fatigue crack. The crack location was between the blade root and tip (the root of the blade stayed in the disk).

As the question states, the accident was in a Southwest Airlines Boeing 737-700. The Aviation Herald says here that it was:


  ...performing flight WN-3472 from New Orleans,LA to Orlando,FL (USA) with 99 passengers and 5 crew, [and] was climbing through FL310 out of New Orleans, about 80nm west of Pensacola,FL (USA) when the front section of the left hand engine (CFM56) separated, debris impacted and punctured the left side of the fuselage causing a loss of cabin pressure. The crew diverted the aircraft to Pensacola for a safe landing on runway 17, the aircraft vacated the runway and taxied to the apron with emergency services following the aircraft. There were no injuries, the aircraft sustained substantial damage.


It also says:


  [In] late Sep 12th 2016 the US NTSB reported, that one fan blade separated from the fan disk during the accident flight, the root of the fan blade remained in the fan hub, however, the rest of the fan blade was missing. The fracture surface of the titanium alloy fan blade, root covered by copper-nickel-indium alloy, showed evidence of a fatigue crack, however no surface or material anomalies were found during initial metallurgic analysis. The engine inlet separated from the engine and impacted fuselage, wing and empanage resulting in a 5x16 inch hole above the left wing.


I expect that's the extent that is publicly available at the moment, because the Aviation Herald report would have been updated if further info was available. So, it's not publicly known if the fatigue crack was low cycle fatigue or high cycle fatigue.

Low cycle fatigue is fatigue caused by large changes in stress amplitude, such as caused by a change in rpm from idle to max speed. Because the change in stress amplitude is large, it can fail in relatively few cycles, compared to HCF. (But still maybe ~10,000). Because it's driven by throttle movements, the number of cycles can be counted. Typically a single flight, even ~10 hours, in a civil aircraft only accumulates less than 10 cycles.

High cycle fatigue is fatigue caused by very small changes in stress amplitude, such as turbulence acting on a blade, every time a rotating blade passes behind a stationary vane. Hence, if a stage in a compressor has 30 vanes, every revolution sees 30 stress cycles on each blade in the following stage. Thus, the number of HCF cycles can accumulate very rapidly. They cannot easily be tracked. Usually, HCF failures need some sort of stress concentration to exist at the point of failure, such as a material anomaly, maintenance damage, or a nick from FOD (foreign object damage from an ingested stone from a runway, for example). HCF failures can require 100,000s of cycles to be accumulated, but if you get 30 every revolution, and the shaft is doing 7,000 rpm in cruise, these accumulate very quickly. Initiation to failure can be just a few flights.

Since there were no material anomalies found on the fracture surface of the blade half they have (the outer piece was not recovered), that indicates the cause of the fatigue crack is unlikely to be a manufacturing issue, and hence a fleet-wide issue.

It is probably an HCF failure, since the crack location does not seem to be in the blade root. Usually, the location of the weakest points due to LCF are in the blade root or fir-tree base, and it sounds like it failed higher than that.

What About The Cowling Failure?

When the fan blade fails, it's pretty violent. Here's a video of a blade-off test done for certification. There is very high vibration at the time of failure, and high vibration while the engine is windmilling before landing. Fan blade failures should not result in cowling failure, because the whole point of the test is to demonstrate that the failure is contained. That means, no part is released at high energy, that may damage the aircraft. Having the cowling fall off, doesn't really align with that philosophy. But, clearly, there is a random element in such an energetic failure.

The most receny fan blade failure I believe was an AirAsia X A330-300 off the west coast of Australia, on Jun 25th 2017. It lost almost the entire blade, but the cowling remained very undamaged, as shown in the picture at the link.

The A380 Air France engine failure that occured in Sept 2017 had similar damage to the aircraft in the question, but the Air France incident was not a fan blade failure. The Airworthiness Directive issued after this states the incident was caused by failure of a fan hub. So, it's not a relevant comparison.

Some aircraft have suffered strutural failings of the fan cowl, without being caused by fan blade failure. Eg. This Egypt Air A330-200 and this China Eastern A330-200 both lost a portion of their cowling. But these failures are a hole blown in the side of the cowling, not loss of the entire duct forward of the fan. These were caused by a structural defect in the composite duct.