All things equal, sending in your applications earlier is better.
Many law schools operate on a rolling admissions basis. So, the earlier you send in your applications, the more seats there are available for incoming students. For this reason, as well as several others, I strongly encourage you to take the LSAT in the June before your senior year if you plan on attending law school directly after you graduate. If you take the test in June, you'll have your score by the end of June/early July and you'll be able to determine at which schools you will be a competitive candidate. You can then focus on writing your personal statement over the summer and get your applications out by October or early November. That is optimal.
Of course, all things typically are not equal and students generally have many competing demands on their time. So, you should organize your time and commitments so as to get the applications in as early as you can given those constraints. Make sure to check application deadlines. Schools vary significantly in terms of deadlines. You absolutely need to get your complete application in prior to the deadline. A complete application includes transcripts and letters of recommendations as well, so make sure you allow time for those to arrive.