This is always a difficult question to answer. On the one hand you want to get re-employed as soon as possible, but if you say that you were fired it might hurt your chances for the job. First, you should ask your employer what information they are going to give to prospective employers. Most employers give very minimal information for fear that if they say the wrong thing they may get sued. I suggest that instead of putting in writing why you got fired I would simply state that you would rather discuss this in person. This will give you a chance to explain the situation. Also you can be general in your reason for leaving; you don’t have to go into detail. Things such as “disagreement with management” may be a true statement without going into great detail.
You should never lie in your interview or application. For one thing if you do get the job you may be terminated if they find out you lied on your application and if you do get into litigation with your ex-employer they will almost certainly be able to get your applications for employment and use those against you at trial.