The local economy is supported by agriculture, with cotton being the most important crop. Wheat, soybeans, milo, and various other crops are also produced in the Lorenzo area.
As of the census of 2000, there were 1,372 people, 472 households, and 353 families residing in the city. The population density was 1,329.3 people per square mile (514.3/km²). There were 525 housing units at an average density of 508.7 per square mile (196.8/km²). The racial makeup of the city was 64.65% White, 6.63% African American, 1.24% Native American, 0.07% Asian, 25.15% from other races, and 2.26% from two or more races. Hispanic or Latino of any race were 54.01% of the population.