Welcome!!! My family lives in the Boston area. I would say lacrosse is going to provide some conditioning itself and MMA on top will just be like cross training and vice versa. If you are doing strength training and cardio with lacrosse you can focus on technique for MMA. Don't get me wrong conditioning for each sport is different. A great example is Hockey alot of running can actually be bad for a hockey players conditioning or just not effective.
Talk to your trainers for MMA 1st, explain what you do and what your goals are for MMA and they should be able to point you in the right direction. If anything I think the circuit training and conditioning rigors of MMA will take your lacrosse game to the next level.