A Lacrosse stick is a rather large item to want to bring on BMQ. I wouldn't recommend taking it along, unless you're prepared to lose it. If you pack it in your duffel, there's a good chance it will get smashed around and broken. If your instructors see it, they could confiscate it and get you in trouble. If you want to risk it, it's your choice, but I certainly wouldn't. I highly doubt you'll have the time to use it. I brought a book on my basic, and never got the opportunity to pick it up in 6 weeks.
As far as what you bring on BMQ; make it as minimal as possible. A few changes of civvy clothes, maybe some writing paper and a book, an alarm clock, some money and that's about it. To give you and idea of what I'm talking about:
1. On my basic, some kid brough a discman and it was stolen. Another kid brought a stereo and it got confiscated by the staff.
2. On my QL3s, a girl wanted to do some studying for university and brough about 10 university textbooks. They were large, heavy and cumbersome. She had to have others carry the bag for her because it was so heavy, and constantly got in $hit because she had no space to store them, and so they were always out. Consequently, she never had the time to open them other than the one weekend off where she chose to stay in the shacks rather than going anywhere. It was a complete waste of time and effort.
Keep that in mind before you pack anything you absolutely don't need. You have enough kit to bring already!