Dear Sue,

Well, I'm not entirely sure what is causing that path in your yard.  It seems to go directly to the tree.  If it were moles, the ground would be spongy in places and you would likely see mounds of dirt. Here is a factsheet that describes what mole damage looks like:

Moles: Damage Management | Natural Resource Stewardship (iastate.edu)

Most lawn diseases are more patchy in nature. Honestly  it looks like something is taking the same path to that tree and has "worn a path".    I have no scientific reason to believe so though, so I won't say that is really much of a possibility. Do you have squirrels? Here is some information on patch diseases of lawns, though I don't think this looks like that.

Managing Patch Disease in Lawns | Lawns | Illinois Extension | UIUC

I will send you an addtional factsheet on lawn care:

This is from Minnesota but provides some timely lawn care information:

Lawn care calendar | UMN Extension

And another from Penn  State:

Lawn Management through the Seasons (psu.edu)

Here is one    discussing dormancy versus death of grass:

Dormancy vs Death – Center for Turfgrass Science (rutgers.edu)

I hope this provides you with some helpful information but I am not sure I really have an  answer to your problem.