Dog & Muddy Patch on Lawn

I would either make a wire netting cage to put over it or flexible plastic type netting which would need to be raised above the muddy patch.

Fence that part off using wire or plastic netting or maybe a long lead to prevent the dog getting to that part.

This is what I do every winter. It's inexpensive and easy to store when not being used. I ordered it online, I don't remember where from.
When the ground is wet the fencing pins can be pushed in without needing a hammer.

Our two cats go to a particular patch of lawn , very brown these days and they dig furiously and roll in it. Always the same part under a blue spruce. Very dry earth, it is like a grey powder. They love it and I just let them go because it gives them such pleasure. They remind me of hippos except it isn’t muddy, just dry earth. Animals are strange sometimes.

Thanks all, I hadn’t thought of fencing the patch off but that’s what I’ll do.
Great idea and Thankyou 😘