Can I legally break my apartment lease early if I believe there is a safety issue here?

You don't specify just what the "safety issue" is. If it's something to do with the apartment itself and constitutes a serious enough situation, such a faulty wiring, then you could break your lease without penalty. You could also repair the prolbem and deduct the cost from your rent or withhold your rent until it is fixed. However, you really need to consult directly with an attorney before undertaking any of these remedies. Additionally, you'll want to contact the fire inspector and/or housing code enforcement officer in your area. They can document the problem which can later be offered as proof in court if necessary.

On the other hand, if the "safety issue" has to do with crime in your complex or neighborhood, things are different. Absent some form of negligence on the landlord's part (i.e. fellow tenants are dealing drugs and the landlord is aware of this but takes no action), you typically can't terminate your lease.

That having been said, you still may not be liable for all of the remaining lease payments. Landlords do have a duty to "mitigate" damages"; that is to minimize their damages by re-letting the premises. This means that if you break the lease, they have to advertise the unit that you vacated and try to find a new tenant. Once they do, they have to let you out of the remainder of the term. However, that will still almost certainly result in your paying for at least a few months more but it may at least give you some financial relief.