Can I continue getting professional back and neck massages after facial and lip fillers?

For
2 weeks following Restylane injection, it's recommended you avoid massage and significant pressure to the
treated area. Although massage to other areas of your body is ok, it may be best
to reschedule your appointment.

Honestly if you position your face well during the massage you are going to put minimal pressure on your mouth, nose and lips.  The biggest risk is with fillers around the cheek bones which could sustain significant pressure with face positioning.  If you feel you really need the benefit of the massage I vote for proceeding carefully. Best of luck.