Generally, you can discharge your lawyer at any point. In fact, in a contingency fee agreement for an accident case in Florida, it states:
Any contingency fee contract must be in writing and you have three (3) business days to reconsider the contract. You may cancel the contract without any reason if you notify you lawyer in writing with three (3) business days of signing the contract. If you withdraw from the contract with the first three (3) days, you do not owe the lawyer a fee, although you may be responsible for the lawyer’s actual costs during that time. But, if you lawyer begins to represent you, your lawyer may not withdraw from the case without giving you notice, delivering necessary papers to you, and allowing time to employ another lawyer. Often, your lawyer must obtain a court approval before withdrawing from a case. If you discharge your lawyer without good cause after the three (3) day period, you may have to pay a fee for the work that the lawyer has done.
Thus, if you cancel within 3 days, then you do not owe that lawyer anything. However, if you cancel after 3 days, then you may have to pay a fee to the lawyer for the work done, assuming you ultimately recover money.