We demonstrate an experimental scheme to simultaneously stabilize the frequency and amplitude of a 3.5 THz third-order distributed feedback quantum cascade laser as a local oscillator. The frequency stabilization has been realized using a methanol absorption line, a power detector, and a proportional-integral-derivative (PID) loop. The amplitude stabilization of the incident power has been achieved using a swing-arm voice coil actuator as a fast optical attenuator, using the direct detection output of a superconducting mixer in combination with a 2nd PID loop. Improved Allan variance times of the entire receiver, as well as the heterodyne molecular spectra, are demonstrated.