@Alexis Monroe - You have 4 parties apparently claiming past or present control of this lot (yourself, previous owner, adjacent lot owner and current renters). I agree that the previous owner is out of the picture due to your purchase. Now you have to untangle what is going on with the other 2 parties.
It seems that you have only received information from the party supposedly renting the lot for storage. I would contact the party said to be collecting the rent. You said you have this party's address so write a concise letter introducing yourself as the property owner and asking for clarification of the situation that enables them to rent out the lot. Send the letter registered mail, return receipt requested.
While waiting for a response talk to the "renters" again and try to get details about the amount of rent paid and any agreement (written or oral) pertaining to their tenancy on your lot. No need to be adversarial at this point - you just want information.
Once the situation is clear to you, brainstorm to devise a solution. Perhaps the rent collector would be interested in purchasing your interest to preserve his rental flow; perhaps the "renters" themselves could purchase the lot to keep their storage space.
Seems to me there are a number of mutually beneficial outcomes if you are careful not to proactively burn any bridges