The first thing I noticed about this shoe was there was no real "outsole" to the shoe. The midsole goes right to the ground, with cuts in the material to give better grip. Through my whole time with this shoe I did not find an issue with the grip on the bottom while running.
When I first got the Lunar Glide 8 I thought the support was less than previous years. After I really started putting miles on, I thought it was pretty comparable to previous versions. It is definitely less support than a shoe like the Ravenna but more support than a shoe like the Ghost or Pegasus.
In (this shoes) retirement it has been good for a walk around shoe. I find the grip on the bottom is not great in the snow or mud when walking around. Again, this is only walking. When I was running in this shoe I never had a problem.