https://extension.oregonstate.edu/ask-extension/featured/how-can-i-naturally-kill-dandelions
https://extension.illinois.edu/lawns/managing-weeds-lawns
The two ways to remove dandelions and other weeds from your lawn is either manually or by the use of herbicides.  If you remove manually, the plants may be disposed of through either composting or by whatever means your area permits for green garden waste.  The easiest and most effective way to eliminate dandelions is by spraying with a herbicide, such as, Trimec or Weed-B-Gon which contains the 3 main herbicides recommended for dandelions.  Do not use Round-up or Glyphosate on your lawn as it will kill the grass as well as the weeds.   In order to minimize the regrowth of dandelions and other weeds in your lawn, it is necessary to crowd out the weeds by promoting a thick and healthy lawn.  This can be done by fertilizing at least 4 times per year (around Easter, Memorial Day, Labor Day, and Halloween) and mowing at a height of 3.5 inches.  This mowing height produces a healthier blade and shades out any seeds trying to germinate during the summer.  If your dandelion crop is very large, you may want to consider having a lawn service treat your lawn for you.  One treatment now and then later this fall will make a huge improvement in your control of the dandelions.