I had the same problem and my father advised for me to use the fertilizer called "bone and blood meal". You can get it at any garden store. I started with cayenne pepper but that only lasted until it rained. After I sprinkled the lawn with the bone and blood meal they haven't returned. They hate the smell of it -- and it's good for your grass!
You can try moth balls. These are toxic to cats and dogs so be careful with them by burying them. Most animals can't stand the fumes.
I had a friend that used to go to the local hunting department and buy some kind of pheromones. A drop on a tag of rag or on a Popsicle stick stuck into the ground in the area ran them off.
Well without killing them and without trapping them your lawn is a lost cause. Trapping them is the best way., just make sure when or if you do you walk to the trap very carefully with a cloth reaching down to the feet. Drape the cloth over the trap, and walk away, placing them into a open aired truck and whisk them away for a couple of miles. Place the trap down, remove the cover carefully !!!! And turn the trap over to release the trap doors. Hope this helps.