I live in NJ. I have rented this apartment for over three years. I did not get a lease renewal this year. I received a promotion and most move out of state. I am a federal employee. My lease ends in Aug. I must report to my new job by May 24. Can I break my lease? Can I get my (substantial) security deposit back?

There is no law that allows you to break your lease without penalty. However your lease may contain a clause allowing you to break it in return for a specific payment, such as a month or two of rent. Read it carefully to see if it mentions anything like that.

If the lease doesn't contain any language allowing you to break it early then I suggest that you speak to the landlord as soon as possible. They may allow you out of the lease in return for a payment or they may allow you to find someone to take over the balance of your lease.