Answer:
The French currently have two territories in the Lesser Antilles - False
France currently has three territories in the Lesser Antilles: Guadeloupe, Martinique, and Saint-Martin.
The British, Dutch, and French have all held territories in the Lesser Antilles - True
Not only they had territories in the Lesser Antilles in the past, they still do.
The British no longer hold territory in the Lesser Antilles - False
The British currently hold three territories in the Lesser Antilles: Anguila, the British Virgin Islands, and Montserrat.
Trinidad and Tobago were the first islands in the Lesser Antilles to gain independence - False
The first of the Lesser Antilles to gain independence was Barbados, in 1966. Trinidad and Tobago only became independent ten years later in 1976.
The Spanish currently have territory in the Lesser Antilles - False
Spain currently holds no territories in the Lesser Antilles. Venezuela, a former Spanish colony does hold territories there, but the country has been independent for two centuries.