Do you have a shiny green "grass" that grows faster than the rest of your lawn and sticks out like a sore thumb? Does it look like the image below? If so, it's actually not a grass, it's a sedge. Nutsedge
Here's a Nutsedge closeup. Notice the shape of the leaf and the triangular stem. Those are the identifying characteristics of Nutsedge.
Sedges are plants that are typically best adapted to growing in poorly drained and tight swamp soils. I usually see nutsedge at its worst when the soil is poorly drained and/or compacted.
There is no great organic control for killing nutsedge in your lawn - other than pulling them very carefully when they're just starting to sprout in the spring. Do this when the soil is moist and you can work to get the entire root including the little nutlet - you'll know it when you see it. If you don't get the entire root parts, the nutsedge will continue to return. But, if you can pull a majority of it effectively, and have healthy strong competitive grasses that you mow nice and high, pulling is one place to start.
There are chemicals available to kill nutsedge without killing your grass. When you use a chemical it's important to remember that you're not doing anything to address the real cause of the problem, you're just treating the sypmtom (the nutsedge). Some chemicals suppress it and others are more effective at killing it. If you're going to use a chemical, you might as well use one that is more likely to kill it. I'm not familiar with all the options but know that Sedgehammer is one that's been around for a while.
When you use a chemical, you're treating the symptom of the problem (the nutsedge) and not doing anything to address the root cause of the problem (poor soil that holds water for extended periods of time). The best way to start to eliminate nutsedtge organically is to eliminate the conditions that are causing it to thrive - poorly drained soil.
It's possible that you might need to redo your lawn and put in physical drain pipes, but we've had success doing multiple applications of Aerify Plus on lawns to help improve the drainage and reduce nutsedge pressure. It's not an instant fix by any means but we've seen a gradual decrease in the nutsedge level where we've done multiple aerivy plus applications over the course of a few seasone. I'd to 2-3 treatments in the spring and another 2-3 in the fall.
The best defense against any type of weed is a thick healthy lawn. In addition to improving your soil and it's drainage, you might want to consider overseeding to thicken up your lawn. Slice Overseeding is one great way to do this.