Here is another picture of the above issue.

Looks to me like either a mole or a vole. Moles dig holes very similar to that and feed on grubs and worms. Voles also dig holes but from what I've read they feed on the roots of grass. I've had plenty of dealings with moles and can say that I've never seen the grass die out like that around their holes so my guess would be you have a vole living in your lawn.

The only thing that is throwing me off the vole track is that there are no visible runs which connect the holes. The grass is only dead in a 2-3 inch ring around each hole. I know the holes are connected by runs, but there is no visible decay of the lawn except where the holes are.

I've only seen one hole so far. It is so large though.

I haven't seen any activity either

If you flood one hole with water does the water come up in another hole?