No, the Florida Lemon Law is for new cards purchased from a dealer.
You may have a fraud claim and perhaps some type of warranty claim based on your sales contract.
If your vehicle was new, less than 24 months old, the answer would be: maybe. However, since your vehicle is nearly 20 years old you have no lemon law rights.
In a private person to person sale of a used car, generally the only obligation on the seller is to answer questions truthfully and not hide anything that they know the buyer would want to know about it. The state lemon law is different from state to state but they almost all require that you be the first retail owner of the vehicle. You can read a summary of what your state's lemon law says here: http://ohiolemonlaw.com/state-lemon-law-summaries.htm. In your case, you need to be able to prove that the seller knew or should have known that the engine was about to fail. If you have a mechanic who can say that, then you may have a claim. You should talk to a consumer law lawyer near you about your legal rights. Call your local attorney bar association and ask for a referral to a consumer law lawyer or you can check online at this web site for one near you: http://www.ohiolemonlaw.com/ocll-site/ocll-locate_local.shtml. The lawyers listed on this page don't pay to get listed and most of them are members of the only national organization of consumer law attorneys. But act quickly because for every legal right you have, there is only a limited amount of time to file a claim or your rights expire and the time limit is different from state to state.