This gives the general information about the license. The simple answer is yes, if you are applying any pesticide (which includes Roundup) to anyone’s property other than your own you need a pesticide license. The type of license will vary depending on which site you are spraying.

If you are a government employee, applying Roundup to turf and ornamentals associated with government buildings, or the owner/employee of businesses who apply Roundup to the turf and ornamental plantings on their business property, you need a Limited Lawn and Ornamental license, unless you are using ready-to-use products (no mixing) purchased from a retail store.

http://www.leg.state.fl.us/statutes/index.cfm?App_mode=Display_Statute&Search_String=&URL=0400-0499/0482/Sections/0482.156.html