Certified GKH Gardening Expert
Those mushrooms are doing their best to help your lawn! They break down organic material and convert it into nutrients. The fruiting bodies are but a tiny portion of the actual mushroom. The rest of it spans, likely, your entire lawn as underground mycelium.
Trying to remove it, not only removes some of the protection of more sinister fungal infections, but the chemicals used will compound and cause the soil to become toxic, as well.
Unfortunately, without gill photos, and a good picture of the base, I am unable to identify the mushroom to its species. I can say with some certainty that it is part of the Genus, Agaricus.
If you do not want the mushrooms in the lawn because they are an eyesore, then taking away the factors that let them present fruiting bodies will be the way to control them. This will mean letting the lawn dry out and removing any shade from the area.
After all is said and done, it will cause much more harm and have no positive effects once removed.
This article will offer some more information:
https://www.gardeningknowhow.com/lawn-care/lgen/eliminate-mushrooms-in-your-lawn.htm
