The attorneys said Arthur Tyler has a history of heart problems and diabetes and risk factors including hypertension, breathing difficulties and being overweight.
A federal court filing Monday in Columbus said Tyler also could suffer adverse reactions from medication he has taken, including blood pressure drugs. Tyler argued lethal injection drugs would amount to cruel and unusual punishment.
The drugs are the only execution method under Ohio law.
Tyler was sentenced to die for killing Cleveland produce vendor Sander Leach during a 1983 robbery.