Anything's possible. In all likelihood, the prosecutor was not lying but rather the Clerk simply hasn't updated the online system yet. You can always contact the State Attorney's Office and ask them because there system may reflect the charges being dropped even if the Clerk hasn't processed the paperwork yet.
This is not to be considered legal advice nor does an attorney-client relationship exist.
If the ASA said he/she was going to dismiss the case then it will most likely happen. The delay could be the clerk in not updating their web site or the ASA waiting for the case to come up on the court calender.
I cannot tell you how this works in Florida, but in Illinois I might get a call from the prosecutor to tell me that the case against my client was going to be dismissed. I would then go to the next set court date expecting that the prosecutor would be there prepared to make a motion for dismissal. In the meantime, I would not expect that the status of the case would change. If I showed up in court and the prosecutor answered ready for trial instead (which would astonish me and has never happened in my own experience) I would expect the judge to grant me a continuance to get ready and bring in my witnesses becasue the prosecutor had, intentionally or not, misled me.. Florida may do things differently, as I defer to any answer you may receive from my local colleagues.
Not sure if this would apply to your case, but courts have held in some jurisdictions that a plea deal reached between prosecutors and defense attorneys, under certain circumstances can be enforced like civil contracts depending on the facts.