Can I still file a bicycle accident lawsuit even if I violated the law or received a ticket?

Yes, you can still file a lawsuit even if you violated the law or received a ticket. First, just because you received a ticket does not mean that you are at fault. A police officer arrives on the scene and he has a very short period of time to assess the situation, talk to a few witnesses, and determine in his best judgement based on the facts he has who's at fault. That does not mean that ultimately in court you will be determined to be at fault. However, if you are determined to have broken the law and have some liability towards the damage, there's something called comparative negligence in the state of Florida, which means even though you may be partially at fault, the other parties may also be at fault and you still may be able to recover for your damages.