We report on the phase locking of a 3.4 THz third-order distributed feedback quantum cascade laser (QCL) using a room temperature GaAs/AlAs superlattice diode as both a frequency multiplier and an internal harmonic mixer. A signal-to-noise level of 60?dB is observed in the intermediate frequency signal between the 18th harmonic of a 190.7?GHz reference source and the 3433?GHz QCL. A phase-lock loop with 7?MHz bandwidth results in QCL emission that is 96% locked to the reference source. We characterize the QCL temperature and electrical tuning mechanisms and show that frequency dependence of these mechanisms can prevent phase-locking under certain QCL bias conditions.