It’s not really a lisp. They use the Spanish “zeta” or z, to replace the s sound. They do it by placing their tongue between their teeth as they enunciate a particular word with the letters s or z in it.
My dad’s side of the family originated from Las Islas Canarias (Canary Islands), before emigrating to Cuba. That is a Spanish territory. My dad actually can speak like a Spaniard really well when he wants to.
My great uncle was an officer under the command of the legendary guerrilla Cuban general Antonio Maceo during the Cuban Independence War. The Cubans fought on horseback with machetes against the Spaniards (which had muskets), and defeated them to gain their independence and freedom from Spain. These warriors were known as Los Mambises, and were tough as nails. My dad was born in the same area that they come from (Bayamo), in a place called Las Minas de Bueycito.
The Rough Riders helped the Mambises during the Cuban Independence War and the term “guajiro” actually was started by the Rough Riders, which referred to the Mambises as war heroes. The Cuban Mambises not being able to speak English would pronounce war hero as “guajiro”, and thus the phrase became a term to describe a Cuban farmer or country folk, since that’s what the ranks of the Mambises were mostly made up of.