No, you may not break your lease for this. The lease is a contract between you and the landlord; as with any other contract, the bad or wrongful acts of third parties does not affect the rights or obligations of the parties to the contract or the contract's legal enforceability. So the neighbor's actions do not allow you to break your contract with the landlord. You could sue the neighbor (including in small claims court) for the value of anything the neighbor has stolen; report the neighbor to the police for theft and the theats; and possibly seek a protective order against the neighbor.