Originally known as Old Fields, it became better known by the name Greenlawn (origin unknown) in the late 1800s. Greenlawn was well known for its pickle production during the 19th century as well as, to a lesser degree, potato and cabbage farms; the principal commodity, pickles, is still celebrated by the annual Pickle Festival, held by the local Greenlawn-Centerport Historical Association at the John Gardiner Farm.
There were 4,499 households out of which 35.8% had children under the age of 18 living with them, 59.3% were married couples living together, 12.1% had a female householder with no husband present, and 25.6% were non-families. 21.6% of all households were made up of individuals and 13.3% had someone living alone who was 65 years of age or older. The average household size was 2.89 and the average family size was 3.38.
In the CDP the population was spread out with 26.0% under the age of 18, 5.8% from 18 to 24, 29.3% from 25 to 44, 23.2% from 45 to 64, and 15.6% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 88.7 males. For every 100 females age 18 and over, there were 83.1 males.
The median income for a household in the CDP was $74,201, and the median income for a family was $76,917. Males had a median income of $58,812 versus $33,727 for females. The per capita income for the CDP was $26,179. About 2.3% of families and 4.5% of the population were below the poverty line, including 4.7% of those under age 18 and 6.6% of those age 65 or over.