… It’s a preposterously easy to find bit of information.
Us fought a war with Spain. Spain lost and got booted from the Americas, Asia and Pacific, with the US taking Guam, Cuba, Puerto Rico and the Philippines.
A few years later we stipulated that Cuba’s independence was conditional on allowing a navel base to remain under US control, Cuba reluctantly agreed, and a lease was signed with no end date with the US paying rent for the land.
When nations change governments, there is always a period of figuring out how treaties and debts are assumed. Usually the successor government assumes at least a portion of “fair” debt inherited from the previous government. (No, we’re not paying for the ammunition the previous government shot at us, yes we’re going to pay the interest on the loan for agricultural supplies). Same goes for treaties.
Post revolution Cuba did the usual and continued international relations as “Cuba”, and not a brand new entity. Hence their argument being that the lease treaty is and was illegitimate, not just “not recognized”, inapplicable or rejected. The US holds it’s a perfectly legitimate agreement and keeps sending payment on time. Everyone agrees there’s an agreement between the US and Cuba around the base, with the contention being about the legitimacy of the 1903 treaty, not it’s applicability.
Yes, Cuba has no leverage to pressure negotiations in their favor. This was true before the embargo as well as after. No, they did not really have a viable alternative to agreeing to the lease. The best option sucking is usually not considered to make a treaty invalid.
Fair or not, the treaty is generally regarded as legitimate, which limits Cuba’s options to use the law to compel the US to leave.
With no interest in negotiation, nothing to offer, no military force, and US complacency with the status quo, the odds of both parties agreeing to end the lease is pretty low.