Certified GKH Gardening Expert
That would be one of the many species of Clavaria. This fungus is busy decomposing lawn litter and grass clippings. This should be considered beneficial to the lawn.
The only way to get rid of them without destroying your lawn will be to take away their food. This means de-thatching your lawn a few times per year, or otherwise removing any debris as it falls onto the yard.
It is a real pain to control them, and no good reason to do so. They replace all of that yard maintenance, while feeding your lawn once the material is decomposed.
Here is an article for more information on keeping mushrooms out of your lawn: