Is it normal to have SIGNIFICANT bleeding while lip filler is being injected?

Minimal bleeding is typical with lip injections.  Increased bleeding can occur if the patient takes blood thinning medications such as ibuprofen, aspirin, vitamin E, etc.  If none of these would have been a factor for you I suggest speaking with your injector about your concerns or finding a more qualified injector next time.  Due to the bleeding you mentioned you may be experiencing more bruising.  Some patients find Arnica and Bromelain helpful after treatment.

There are both patient factors and injector factors that can affect how much you bleed during the procedure. Generally speaking, there is very little blood loss with lip injections in most cases.   You should avoid products or medication that can potentially thin your blood prior to the procedure. These include fish oil, aspirin, ibuprofen, and other NSAIDS.  There are also medical reasons why some patients are more prone to bleeding than others.  However you would typically be aware of these conditions prior to lip injections due to more than normal bleeding with minor cuts.  These patients might also have a history of easy bruising.   Patients with bleeding disorders generally have been diagnosed earlier in life.   It sounds like you have had some injections that did not bleed as much as your last treatment from the new injector. This indicates that technique was possibly involved. I would recommend that you go to an experienced injector. Although bruising and bleeding can occur from any injector, what you have described is not typical.  Icing the lips prior to treatment can also help reduce bruising and bleeding. Best wishes!