I played around with the GPS yesterday and took it out for a run and you do not have to use the LG Health app.
Now most of the popular apps do depend on the phone's GPS but I found 2 apps that would work without the phone. Ghostracer worked very well, GPS seemed to lock in pretty quickly and the mapping was accurate. Runkeeper is supposed to work as well but in my quick test the mapping was not very accurate. I will have to test on a real run another time. I normally use Strava but it would not work without the phone. I had never heard of it before but it looks like Ghostracer is the answer so far since it works without the phone and can sync automatically to Strava or Runkeeper.
I can't really figure out the benefit of the LG Health app. How do I get the results back to the phone? Where do I see the map of my run?
I will test Runkeeper again, then probably Runtastic, MapMyRun and Endomondo.