The answer is yes, the police are allowed to lie to you to get you to confess. The law in Florida is that the use of tricks or factual misstatements by the police do not by themselves make a confession involuntary.
For instance, in one Florida Supreme Court case called Burch versus State of Florida, an individual accused of murder was questioned by the police for more than five hours. During those several hours, the police presented false evidence to Mr. Burch in order to get him to confess. He was also given a false polygraph test and then told that he had failed that test. Eventually Burch confessed to the murder.
Burch later tried to get his confession thrown out by arguing that the tricks used by the police were illegal and that such tricks caused him to confess involuntarily.
In rejecting Burch's argument, the Florida Supreme Court pointed out that Burch was fully advised of his Miranda rights, he never asked to leave the sheriff's office, he never asked for a lawyer, he never asked the police to stop questioning him, and he was not physically coerced by the police.
It is because of cases like this that I almost always advise people not to speak with the police but to instead have their lawyer do their talking for them.