Question
How do I kill the witch grass in my lawn without killing my lawn?

Answer
You wish to kill a true grass (Panicum spp.)in a true grass. This is going to be very difficult. My suggestion is to mow the lawn frequently enough to prevent the witch grass from seeding. This might mean mowing even when the lawn has not grown enough to make mowing it meaningful. But it is essential to the program to stop the production of weed seeds now! If you cannot get to it often enough and witch grass produces some seed heads, then bag the clippings and discard them or compost them thoroughly. The next attack is focused on the seeds already in the ground. You want to prevent them from germinating. To achieve this, you can apply a pre-emergent chemical before the conditions start to favor seed germination in the spring. When the temperature starts to get up to 70 degrees, around the clock, seeds generally wake up and start to to think about growing. You want the pre-emergent chemical on the ground before that happens.
But not too long before. Because the chemical will break down as time goes by and the temperature goes up. If all goes well, you will not need to make a second application. But if you judge that the chemical has broken and the label might permits it, go ahead and make a second application. I'd like to stress that it is critical to the success of your efforts that the pre-emergent program is given the best chances to work. The chemical, all of it, must get into the top layer of the soil and stay there. Use enough water to get it there (off the leaves of the lawn grass and through the thatch layer). Cut back irrigation to the minimum duration to prevent runoff which will carry away some of that precious chemical.
Last of all, settle in for the long haul. The battle can be considered won if very few or no witch grass is evident in the second year.
The war on weeds goes on.