The plant you have is yarrow, which has a fern-like leaf but is not a fern.  It is a difficult weed to control.  Your best options are to keep the lawn moist and well-fertilized which will give it a competitive advantage.  Another option is to dig it out, but in order to be successful all of the rhizomes must be removed, which is hard to do.  If you leave any behind they will just start new plants.  Yarrow also does not like shade.  

For current chemical control options, please contact your county weed supervisor.