If the tracks are under the lawn in the soil as you say, then it is probably moles.  If these tracks are on the surface and have only become obvious since the snow has melted then it is voles.  Either way, an application of Mole0Max rodent repellent will chase either pest out of the area.  Neither of these critters eat grass roots though.  The voles might have nibbled the blades off but the roots are fine and the grass will grow back quickly.  Moles don’t eat plants, just earthworms and soil grubs.