Trumpet Vines are a beautiful plant but can be a real problem.  About the only think you can do is to spray the sprouts that pop up in the lawn with a weed killer like Weed Beater Ultra or Bonide Chickweed and Clover Killer.  Avoid Round-up or Kleen-up as they will kill the lawn as well as the errant trumpet vine.  This will knock back the shoots but never eliminate the problem.  Since they are originating as suckers from the original plant, more will always appear.  Regularly mowing the shoots that appear also helps control them but this will be an ongoing battle.