Regarding the basis for the Cuban lease

The USA may use the property at Guantanamo only as a naval station.

The lease agreement states that the purpose of the lease is to help the USA protect Cuba from a military threat to its independence.

The Bay of Pigs was an action undertaken that was inconsistent with that agreement. The US actions were not directed to protect the new Cuban government, but to overthrow it. This failure to come to the aid of the new Cuban government gives rise to a claim for damages. Years later, Kennedy promised to respect Cuban integrity, a promise that fell far short of the understanding that the USA would help to protect Cuba's independence from foreign military aggression. This is an anticipatory breach.

The US recognized that the Castro regime was the legitimate government of Cuba, since in 1959 the USA sent a check to the Castro regime, purportedly as payment under the lease. Further, the USA claims that the cashing of the check, in 1959, by the Castro regime constitutes the completion of a valid transaction required by the lease.