Does the state of Florida have a labor law on employers having to give a lunch break after a certain peroid of time?

My research indicates no.

U.S. Department of Labor - Employment Standards Administration (ESA) - Wage & Hour Divisions (WHD) - Minimum Paid Rest Period Requirements Under State Law for Adult Employees in Private Sector - January 1, 2008 (http://www.dol.gov/esa/whd/state/rest.htm#Florida)

The law requires a break if you work 6 to 8 hours but for the most part there isn't specific laws on breaks or lunches.
I think that some states say two 10 to 15 minute breaks or a lunch break

No it does not.