Can the trustee of a q tip trust dissolve the trust before the demise of the lifetime beneficiary without the consent of the residual beneficiaries in the state of New Jersey?

A trustee has only the powers that are provided in a trust instrument. Since a Q Tip Trust is created in a will by a testator who desires to preserve the trust property for his children, it is doubtful a testator would grant the power to dissolve the trust to the trustee. Therefore, if the will did not specifically grant that power to the trustee the answer to your question is no.