It is possible to organically rid a lawn of clover. Clover grows in areas of a lawn where nitrogen levels are low and restores nitrogen back into the grass. One way to get rid of clover is by physically removing it and tilling the soil.
The tilling causes aeration, which will prepare the soil for new growth of healthy grass. Organic compost should be added to the soil, followed by grass seed. Watering the lawn as needed will encourage new grass to grow where the clover once was. This can take between 3 and 30 days, depending on the grass seed type.