While that is a pretty sparse lease, there looks to be enough there... parties identified, sufficient property description, amount of consideration and such that I'd expect a judge to hold it enforceable.
If you are buying the property, then you are buying it subject to the lease (which is proper term, not assuming the lease). That means his lease is still enforceable against the new owner.
Now if you want to terminate the lease and he doesn't agree, then you would need a legal reason. Typically the legal reason used is non-payment of rent but there are others such as violating another provision of the lease, like using the property for a use prohibited by the lease.
Take a look at
Florida Statute 83.20.
Unfortunately the lease lacks any sort of restrictions or rules for the tenant to break so you would need to have a reason like using the property for an illegal purpose like storing drugs there or creating a nuisance with bad smells or excessive noise or some sort of county health code violation. Well, you get the idea.
Also, if they are doing something they shouldn't be which gives you a reason to terminate the lease, they have to be given 15 days written notice which gives them a chance to cure the violation.